tag:blogger.com,1999:blog-67167985115177209942024-02-06T18:50:08.846-08:00All about actuarial scienceAnonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-6716798511517720994.post-76947280179887576182012-04-30T04:14:00.001-07:002012-04-30T04:14:57.685-07:00TEMPORARY LIFE ANNUITIES<div dir="ltr" style="text-align: left;" trbidi="on">
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Life annuities may be either temporary life annuities or
whole life annuities. Both kinds have many practical uses in actuarial
calculations. In a temporary life annuity, each payment is made only if a
designated person is then alive, but the payments are limited to a fixed number
of years. In a whole life annuity, the payments continue for the entire
lifetime of a designated person.</div>
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There are also temporary life annuities in which the first
payment is made at the beginning, that is, on the same date on which the
present value is calculated. These are known as <i>temporary life annuities due.</i> The use of the word “due” is
comparable to its use in annuities certain. This type of annuity is important
in life insurance calculations, because premiums payable for a life insurance
policy represent an annuity due.</div>
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<o:p></o:p></div>
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The line diagram of two five payments life annuities, one
immediate and one due, look like this:<o:p></o:p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyXLcDnmdiCS9taqQPd2NO-ZZ5uplqmjs5Fa0zSVx8DkCVxljURnvTEA3pTnArwooE2d3NHHsYiP9L0e57hZfOzkJFIccVLGE-71jquMAJ4u88MQnc1iyfi4oOqQdqa4LFlTMje-vB3wgg/s1600/temporary+life+annuity.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyXLcDnmdiCS9taqQPd2NO-ZZ5uplqmjs5Fa0zSVx8DkCVxljURnvTEA3pTnArwooE2d3NHHsYiP9L0e57hZfOzkJFIccVLGE-71jquMAJ4u88MQnc1iyfi4oOqQdqa4LFlTMje-vB3wgg/s1600/temporary+life+annuity.PNG" /></a></div>
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<b><i><span style="font-size: 12pt;"><br /></span></i></b></div>
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<b><i><span style="font-size: 12pt;">To Illustrate</span></i>: </b>Using the given table
and 5% interest, calculate the present value at age 30 of a three – year life
annuity due of $100 per year.<o:p></o:p></div>
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<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; margin-left: 99.9pt; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Age
(x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: Calibri, sans-serif;"><span style="font-size: 15px; line-height: 17px;">l</span><span style="line-height: 17px;"><span style="font-size: xx-small;">x</span></span></span></div>
</td>
</tr>
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<b>30<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9480358<o:p></o:p></div>
</td>
</tr>
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<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>31<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9460165<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>32<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9439447<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>33<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9418208<o:p></o:p></div>
</td>
</tr>
</tbody></table>
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Values of <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWR-VjTZ-oAz68spLllxzms56i_NoLveFNVNGogfKoqY-PrOpu4LuDWfcHbcd5UlBG8ZzgjVwkNiUcSbKv40cv3D9gKLXsNj-6kGLcUTA3k2ziNfXtcKY476pmMjH0GytGh4t8JRWbxL60/s1600/present+value+of+a+life+annuity8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWR-VjTZ-oAz68spLllxzms56i_NoLveFNVNGogfKoqY-PrOpu4LuDWfcHbcd5UlBG8ZzgjVwkNiUcSbKv40cv3D9gKLXsNj-6kGLcUTA3k2ziNfXtcKY476pmMjH0GytGh4t8JRWbxL60/s1600/present+value+of+a+life+annuity8.PNG" /></a>at 5% interest are as follows:</div>
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<o:p></o:p></div>
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<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>n<o:p></o:p></b></div>
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<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 157.5pt;" valign="top" width="210"><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWXtDjpTglq__EgpenFeKmpc1jY8pIf-5V1K5bp2GSxTKxroI_Uf-mF7p109wuMBN-U-GgoROfouTtkyW4qx9n4-zr1RX8JzCij7bBYLD_kU3TpJEsJNQigK3SGVUipIRDqt7hTdOO1n81/s1600/temporary+life+annuity1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWXtDjpTglq__EgpenFeKmpc1jY8pIf-5V1K5bp2GSxTKxroI_Uf-mF7p109wuMBN-U-GgoROfouTtkyW4qx9n4-zr1RX8JzCij7bBYLD_kU3TpJEsJNQigK3SGVUipIRDqt7hTdOO1n81/s1600/temporary+life+annuity1.PNG" /></a></div>
</td>
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<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>1<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 157.5pt;" valign="top" width="210"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.952381<o:p></o:p></div>
</td>
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<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>2<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 157.5pt;" valign="top" width="210"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.907029<o:p></o:p></div>
</td>
</tr>
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<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>3<o:p></o:p></b></div>
</td>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 157.5pt;" valign="top" width="210"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.863838<o:p></o:p></div>
</td>
</tr>
</tbody></table>
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<b><i><span style="font-size: 12pt;">Solution:<o:p></o:p></span></i></b></div>
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The line
diagram for this life annuity due appears as follows:<o:p></o:p></div>
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<b> $ 100 $ 100 $ 100</b></div>
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<span style="height: 15px; margin-left: 479px; margin-top: 1px; position: absolute; width: 2px; z-index: 251673600;"><img height="15" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" v:shapes="_x0000_s1029" width="2" /></span><span style="height: 15px; margin-left: 370px; margin-top: 1px; position: absolute; width: 2px; z-index: 251672576;"><img height="15" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_s1028" width="2" /></span><span style="height: 15px; margin-left: 255px; margin-top: 1px; position: absolute; width: 2px; z-index: 251671552;"><img height="15" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif" v:shapes="_x0000_s1027" width="2" /></span><span style="height: 2px; margin-left: 161px; margin-top: 7px; position: absolute; width: 320px; z-index: 251670528;"><img height="2" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif" v:shapes="_x0000_s1026" width="320" /></span><b><sup>Temporary
life annuity due</sup> *<o:p></o:p></b></div>
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<b><br /></b></div>
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<b>
Age 30 31 32 33<o:p></o:p></b></div>
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<b><br /></b></div>
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The
expression for the present value will have a numerator representing the total
to be paid out to the survivors at each age with each such amount being
discounted at interest to the evaluation date. The first payment is due upon
the evaluation date. Hence, its present value is simply $100 (<span style="font-family: Calibri, sans-serif;"><span style="font-size: 15px; line-height: 17px;">l</span><span style="line-height: 17px;"><span style="font-size: xx-small;">30</span></span></span>); it is not multiplied
by any discounting factor. The denominator is the number living at the
evaluation date:<o:p></o:p></div>
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Basic
equation:<o:p></o:p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNKBK2znTI6MmSBGhKxaT2v9epbvVnm7o3BmrNIVAvGwlnTP9XFtJw207_yh4lqFhcGT4qlJppAEQuB36Cq3VKXqbKI9v3Dve1oh2VWlyEsSxIAB0YPtW8Q0OL_NBUSqAcSsfWARj6TF3T/s1600/temporary+life+annuity2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNKBK2znTI6MmSBGhKxaT2v9epbvVnm7o3BmrNIVAvGwlnTP9XFtJw207_yh4lqFhcGT4qlJppAEQuB36Cq3VKXqbKI9v3Dve1oh2VWlyEsSxIAB0YPtW8Q0OL_NBUSqAcSsfWARj6TF3T/s1600/temporary+life+annuity2.PNG" /></a></div>
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Present
Value = $ 285.35<o:p></o:p></div>
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The
present value of annuity immediate of the same question must be less than the
present value of the life annuity due ($285.35), because each payment in the
annuity immediate is paid one year later than its counterpart in the annuity
due. Hence, there is a smaller probability that it will have to be paid, and
there are a greater number of years in which interest is earned.<o:p></o:p></div>
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<b><i><span style="font-size: 12pt;">To Illustrate</span></i></b>: </div>
<div class="MsoNormal">
Calculate the present
value at age 65 of a four year temporary life annuity due of $50 per year? (Use
given table and 6% interest)<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: Calibri, sans-serif;"><span style="font-size: 15px; line-height: 17px;">l</span><span style="line-height: 17px;"><span style="font-size: xx-small;">x</span></span></span></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>65<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9019487<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>66<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8935696<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>67<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8847340<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>68<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8753363<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>69<o:p></o:p></b></div>
</td>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8652385<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-align: left;">
Values
of <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh2_VqaHUrRchwreLuMzEv6JcWP_diy-7vO3cyiqXEz28D-iyHjBnW5sx5VlNrc84AMLUKCcdQBrl5KubamVgbkpv4wfYjV5HuG0xZX_05CKlf6NRb_K8mLVGC1PMXP6Br1AGaLLXYRh0I/s1600/present+value+of+a+life+annuity8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh2_VqaHUrRchwreLuMzEv6JcWP_diy-7vO3cyiqXEz28D-iyHjBnW5sx5VlNrc84AMLUKCcdQBrl5KubamVgbkpv4wfYjV5HuG0xZX_05CKlf6NRb_K8mLVGC1PMXP6Br1AGaLLXYRh0I/s1600/present+value+of+a+life+annuity8.PNG" /></a>at 6% interest are as
follows:</div>
<div class="MsoNormal" style="text-align: left;">
<br /></div>
<div class="MsoNormal" style="text-align: left;">
<o:p></o:p></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 141.75pt;" valign="top" width="189"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>n<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 140.65pt;" valign="top" width="188"><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjamMtRuFMcE1tbsrO_fKonf5fNk0zBJgDH-rrity7hA5no_1HYqu_n6Mw1kViksjetc-b8ioZkjta_GwXRjT2tETxKB8g7QTYHUsq2IS0FPf4PAgS4lU7uYiCBz9c6FHm_ZInB5bs32_p/s1600/temporary+life+annuity1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjamMtRuFMcE1tbsrO_fKonf5fNk0zBJgDH-rrity7hA5no_1HYqu_n6Mw1kViksjetc-b8ioZkjta_GwXRjT2tETxKB8g7QTYHUsq2IS0FPf4PAgS4lU7uYiCBz9c6FHm_ZInB5bs32_p/s1600/temporary+life+annuity1.PNG" /></a></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 141.75pt;" valign="top" width="189"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>1<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 140.65pt;" valign="top" width="188"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.943396<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 141.75pt;" valign="top" width="189"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>2<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 140.65pt;" valign="top" width="188"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.889996<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 141.75pt;" valign="top" width="189"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>3<o:p></o:p></b></div>
</td>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 140.65pt;" valign="top" width="188"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.839619<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="text-align: left;">
<b><i><span style="font-size: 12pt;">Solution:<o:p></o:p></span></i></b></div>
<div class="MsoNormal" style="text-align: left;">
The
line diagram for this life annuity due appears as follows:</div>
<div class="MsoNormal" style="text-align: left;">
<br /></div>
<div class="MsoNormal" style="text-align: center;">
<b>$ 50 $ 50 $ 50 $ 50</b>
</div>
<div class="MsoNormal" style="text-align: left;">
</div>
<div style="text-align: center;">
_______________________________________________</div>
<o:p></o:p><span style="position: relative; z-index: 251678720;"><span style="height: 19px; left: 434px; position: absolute; top: -1px; width: 2px;"><img height="19" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif" v:shapes="_x0000_s1030" width="2" /></span></span><span style="height: 2px; margin-left: 45px; margin-top: 6px; position: absolute; width: 391px; z-index: 251674624;"></span><br />
<b><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">Age 65 66 67 68 69</span></b></div>
<div style="text-align: center;">
<span style="font-family: Calibri, sans-serif;"><span style="font-size: 15px; line-height: 17px;"><b><br /></b></span></span></div>
<div style="text-align: left;">
<div class="MsoNormal">
Basic
equation:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4ADmDuikF_meZA8FFQrmlQphNf6QqG5jbCE-j8bt8b3YIKUTDNYFrmpQDRH0DcqJE_ATIxwhXFtdtS-KhpxjP9aHpOZKDqP4iED_AQCk_sJQ6N0iwlcyGBgl1pQgFVxpRbtGeX5mWxhNW/s1600/temporary+life+annuity3.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4ADmDuikF_meZA8FFQrmlQphNf6QqG5jbCE-j8bt8b3YIKUTDNYFrmpQDRH0DcqJE_ATIxwhXFtdtS-KhpxjP9aHpOZKDqP4iED_AQCk_sJQ6N0iwlcyGBgl1pQgFVxpRbtGeX5mWxhNW/s1600/temporary+life+annuity3.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
</div>
<br />
<br />
<br />
<br /></div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com2tag:blogger.com,1999:blog-6716798511517720994.post-78781267557048653152012-04-27T11:18:00.000-07:002012-04-29T04:44:37.652-07:00PROBABILITIES INVOLVING MORE THAN ONE EVENT<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
<div class="MsoNormal">
Probabilities involving more than one event may be
calculated using the Addition Rule and Multiplication Rule. Those are as
follows:<o:p></o:p></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<a name='more'></a><br />
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; line-height: 115%;">ADDITION RULE:</span></b></div>
<div class="MsoNormal">
If there are several possible events, but only one could occur at any
one time, the probability that one of such events will actually occur at a
given time is the total of the probabilities of each individual event happening
at that time.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<o:p></o:p><b><span style="font-size: 14.0pt; line-height: 115%;">MULTIPLICATION RULE:<o:p></o:p></span></b></div>
<div class="MsoNormal">
If
several events are independent (that is occurrence of any one has no effect on
the probability of the occurrence of the others), the probability that all of
the events will happen is represented by multiplying the probabilities of the
individual events together.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">To Illustrate</span></i></b>:
Using the following portion of a mortality table, calculate the probability
that a person age 40 will die either at age 60 or at age 61.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;" valign="top" width="138">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
l<sub>x</sub><b><o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 99.0pt;" valign="top" width="132">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
d<sub>x</sub><b><o:p></o:p></b></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;" valign="top" width="138">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>40<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
97353<o:p></o:p></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 99.0pt;" valign="top" width="132">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
198<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;" valign="top" width="138">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>41<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
97155<o:p></o:p></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 99.0pt;" valign="top" width="132">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
216<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;" valign="top" width="138">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 99.0pt;" valign="top" width="132">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;" valign="top" width="138">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>60<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
84650<o:p></o:p></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 99.0pt;" valign="top" width="132">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1325<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;" valign="top" width="138">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>61<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
83325<o:p></o:p></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 99.0pt;" valign="top" width="132">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1406<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 103.5pt;" valign="top" width="138">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>62<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
81919<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 99.0pt;" valign="top" width="132">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1491<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">Solution: <o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Since only one of the events can occur, the Addition Rule
that two individual probabilities are added is applicable. The probability that
a person age 40 will die during the year he or she is age 60 is equal to the
number of people dying at age 60 divided by the number living at age 40:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>Basic equation:</i></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
Probability of Dying at Age 60) <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZqCYbLRd-3MI7nN7sWMA9XXXUJIdfx0XQt55R0mtD7uzktr7wOlgw4unJE0LF_vPjNv4rMCe0yn73ekSQpm-lktcKcppdcF3R5Fh9h9g0VdDu6u1W5KcHdh-T7YRU3IUsYmzMD6PP5k64/s1600/probabilities+involving+more+than+one+event.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZqCYbLRd-3MI7nN7sWMA9XXXUJIdfx0XQt55R0mtD7uzktr7wOlgw4unJE0LF_vPjNv4rMCe0yn73ekSQpm-lktcKcppdcF3R5Fh9h9g0VdDu6u1W5KcHdh-T7YRU3IUsYmzMD6PP5k64/s1600/probabilities+involving+more+than+one+event.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Substitute the values from the given
table:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
(Probability
of Dying at Age 60) <span style="line-height: 115%;">=</span><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>1325</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast'><m:r>97353</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 28.5pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span><span style="line-height: 115%;">1325/97353</span></div>
<div class="MsoNormal">
(Probability of Dying at Age 60) = 0.0136</div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
Similarly, the probability that a person age 40 will die
during the year he or she is age 61 is<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>Basic equation:<o:p></o:p></i></div>
<div class="MsoNormal">
</div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="text-align: left;">(Probability of Dying at age 61) =</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5eTiX63nPWrH9R4PeNwVB3AuKRT6D4eM3dfv5A3mISKwl3HxiyQ5d_ElXlH35TokjJod00PLjleJyKizRgMazrbdiMNLCr61xJQMquCvrTp73SEXejNRuECjCUANErgAeGoTT86POugoh/s1600/probabilities+involving+more+than+one+event1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5eTiX63nPWrH9R4PeNwVB3AuKRT6D4eM3dfv5A3mISKwl3HxiyQ5d_ElXlH35TokjJod00PLjleJyKizRgMazrbdiMNLCr61xJQMquCvrTp73SEXejNRuECjCUANErgAeGoTT86POugoh/s1600/probabilities+involving+more+than+one+event1.PNG" /></a></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
</div>
<div class="MsoNormal">
Substitute the values from the table<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
(Probability of Dying at age 61) <span style="line-height: 115%;">=</span><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span><span style="line-height: 115%;">1406/97353</span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math","serif";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>1406</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast'><m:r>97353</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><v:stroke joinstyle="miter"><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"><v:f eqn="sum @0 1 0"><v:f eqn="sum 0 0 @1"><v:f eqn="prod @2 1 2"><v:f eqn="prod @3 21600 pixelWidth"><v:f eqn="prod @3 21600 pixelHeight"><v:f eqn="sum @0 0 1"><v:f eqn="prod @6 1 2"><v:f eqn="prod @7 21600 pixelWidth"><v:f eqn="sum @8 21600 0"><v:f eqn="prod @7 21600 pixelHeight"><v:f eqn="sum @10 21600 0"></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas><v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"><o:lock aspectratio="t" v:ext="edit"></o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 26.25pt; width: 28.5pt;" type="#_x0000_t75"><v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"></v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></div>
<div class="MsoNormal">
(Probability of Dying at age 61) = 0.0144<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The desired probability equals the total of the two
individual probabilities:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The equation is:<o:p></o:p></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:eqArr><m:eqArrPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:eqArrPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>Probability</m:r><m:r>
</m:r><m:r>of</m:r></span></i></m:e><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>Dying</m:r><m:r>
</m:r><m:r>at</m:r><m:r> </m:r><m:r>Ag��</m:r></span></i><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
mso-bidi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:e><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";mso-fareast-font-family:
"Cambria Math";mso-bidi-font-family:"Cambria Math"'><m:r>60 </m:r><m:r>or</m:r><m:r>
61</m:r></span></i></m:e></m:eqArr></m:e></m:d></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 38.25pt; width: 84.75pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--> </div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAwZwxXgtGz3zu3jfr0sm1XttvnuPsgxXbODF69wxIaDWGZ8J9Vth4TNGxLCt8ZszSRzWwY7TehQSPBALYCjB_2QAIvmycZkC-vROHftvHRAaW3kS2ALkzICYXurq0uNj7lwXkFYK6XUmI/s1600/probabilities+involving+more+than+one+event2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAwZwxXgtGz3zu3jfr0sm1XttvnuPsgxXbODF69wxIaDWGZ8J9Vth4TNGxLCt8ZszSRzWwY7TehQSPBALYCjB_2QAIvmycZkC-vROHftvHRAaW3kS2ALkzICYXurq0uNj7lwXkFYK6XUmI/s1600/probabilities+involving+more+than+one+event2.PNG" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
</div>
<div class="MsoNormal">
Hence, 0.0280 is the probability that a
person age 40 will die either at age 60 or 61.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">To Illustrate</span></i></b>:
Using the following portions of a mortality table, calculate the probability
that a mother age 55, and her daughter, age 25 will both live at least 15 more
years.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
l<sub>x</sub><b><o:p></o:p></b></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>24<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9953<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>25<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9947<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>26<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9940<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<br /></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>39<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9827<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>40<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9814<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>41<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9801<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>54<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9444<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>55<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9388<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>56<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9327<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>.<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
.<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>69<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
7885<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>70<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
7717<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.75in;" valign="top" width="168">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>71<o:p></o:p></b></div>
</td>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.0pt;" valign="top" width="156">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
7539<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<o:p><br /></o:p></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Solution:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Assuming that one event has no effect on
the other, the Multiplication Rule, that two individual probabilities are
multiplied is applicable. For mother;<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>Basic
equation:<o:p></o:p></i></div>
<br />
<div class="MsoNormal">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRRHE-UpmYzr7lIdRPtF1Sl_T7Ue-L-WkK6Msxggf5RmYMcP0Lwwc0z0wbUNYqCoy5KpppLx8zIALo1RU3Scsr6mUq4GtTMj09_anVRSMZwyBq1f69Jv8X4Pcdk4OyRjr2eD_nr6eNzWwm/s1600/probabilities+involving+more+than+one+event3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRRHE-UpmYzr7lIdRPtF1Sl_T7Ue-L-WkK6Msxggf5RmYMcP0Lwwc0z0wbUNYqCoy5KpppLx8zIALo1RU3Scsr6mUq4GtTMj09_anVRSMZwyBq1f69Jv8X4Pcdk4OyRjr2eD_nr6eNzWwm/s1600/probabilities+involving+more+than+one+event3.PNG" /></a></div>
<div class="MsoNormal">
<b><u><br /></u></b></div>
<div class="MsoNormal">
<b><u>For
Daughter:</u></b></div>
<div>
<div class="MsoNormal">
<b><u><br /></u></b></div>
<i><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">Basic equation</span></i></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYj3-QEB_mBZe8kfwiZzzYAbVBCzITYwyhVxIzy3z9EykMsEQ7MkD1uKRQI9zcR2t6zXVp70R5HnwODRp9NWYMM6IdqFCCqvoU1I1-uvVzn70pRKtn1t48a9AA_jkESyldgyGcBKrptZUL/s1600/probabilities+involving+more+than+one+event4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYj3-QEB_mBZe8kfwiZzzYAbVBCzITYwyhVxIzy3z9EykMsEQ7MkD1uKRQI9zcR2t6zXVp70R5HnwODRp9NWYMM6IdqFCCqvoU1I1-uvVzn70pRKtn1t48a9AA_jkESyldgyGcBKrptZUL/s1600/probabilities+involving+more+than+one+event4.PNG" /></a></div>
<div>
<i><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><br /></span></i></div>
<div>
<div class="MsoNormal">
The desired probability that both will
live at least 15 years equal the two individual probabilities multiplied
together:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The equation is:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuIfCWDmrhyphenhyphen2E1PlyUOr6v5HHafWPRpwHJQFvjy9v43byoM2p9djFGS_hM-zXxG5apZngHP2XfMPBmaaoj3EYG1-GbbE2UHjoe4BUH6paIn0EliEke7YrtTNEPYUFTs4WYAh73ojwIF1yU/s1600/probabilities+involving+more+than+one+event5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuIfCWDmrhyphenhyphen2E1PlyUOr6v5HHafWPRpwHJQFvjy9v43byoM2p9djFGS_hM-zXxG5apZngHP2XfMPBmaaoj3EYG1-GbbE2UHjoe4BUH6paIn0EliEke7YrtTNEPYUFTs4WYAh73ojwIF1yU/s1600/probabilities+involving+more+than+one+event5.PNG" /></a></div>
<div class="MsoNormal">
<!--[if gte msEquation 12]><m:oMath><m:d><m:dPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
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normal'><m:ctrlPr></m:ctrlPr></span></m:eqArrPr><m:e><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>Probability</m:r><m:r>
</m:r></span></i></m:e><m:e><i style='mso-bidi-font-style:normal'><span
style='font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast'><m:r>Bot</m:r><m:r>h</m:r><m:r> </m:r><m:r>Live</m:r></span></i></m:e></m:eqArr></m:e></m:d></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.5pt; position: relative; top: 10.5pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 24.75pt; width: 70.5pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><!--[endif]--> <o:p></o:p><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">The result shows that the probability that a
mother, age 55, and her daughter, age 25, will both live at least 15 more years
is 0.8110.</span></div>
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYj3-QEB_mBZe8kfwiZzzYAbVBCzITYwyhVxIzy3z9EykMsEQ7MkD1uKRQI9zcR2t6zXVp70R5HnwODRp9NWYMM6IdqFCCqvoU1I1-uvVzn70pRKtn1t48a9AA_jkESyldgyGcBKrptZUL/s1600/probabilities+involving+more+than+one+event4.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYj3-QEB_mBZe8kfwiZzzYAbVBCzITYwyhVxIzy3z9EykMsEQ7MkD1uKRQI9zcR2t6zXVp70R5HnwODRp9NWYMM6IdqFCCqvoU1I1-uvVzn70pRKtn1t48a9AA_jkESyldgyGcBKrptZUL/s1600/probabilities+involving+more+than+one+event4.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYj3-QEB_mBZe8kfwiZzzYAbVBCzITYwyhVxIzy3z9EykMsEQ7MkD1uKRQI9zcR2t6zXVp70R5HnwODRp9NWYMM6IdqFCCqvoU1I1-uvVzn70pRKtn1t48a9AA_jkESyldgyGcBKrptZUL/s1600/probabilities+involving+more+than+one+event4.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a></div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-15747730166273381262012-04-27T10:13:00.001-07:002012-04-27T10:13:40.045-07:00PRESENT VALUE OF A LIFE ANNUITY<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As stated earlier, an annuity is a series of payments and
the present value of the annuity is the total of the present values of each of
the individual payments. To find the present value of a series of payments where
each payment is made only if the designated payer or recipient is alive to pay
or receive it, we can now use the method for calculating the present value of a
single payment.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">For Example</span></i></b>:
The present value at age 35 of a life annuity of $100 per year for three years
(with the first payment due at age 36) can be represented by the following line
diagram:<o:p></o:p><br />
<br />
<a name='more'></a><br /></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHVY1eOH9peOSHZHrxefCnBVQXc365gUNLb6aQwGbBMrrTo3S9tg7xqO4rCUz8_yIWCkJyukvlDKsiaHg7AsjunK0dpcFtItBSqGP5APqNNU71ut_NhWGeN5sKO2rPq_2aI-K6tkn7sImT/s1600/present+value+of+a+life+annuity.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHVY1eOH9peOSHZHrxefCnBVQXc365gUNLb6aQwGbBMrrTo3S9tg7xqO4rCUz8_yIWCkJyukvlDKsiaHg7AsjunK0dpcFtItBSqGP5APqNNU71ut_NhWGeN5sKO2rPq_2aI-K6tkn7sImT/s1600/present+value+of+a+life+annuity.PNG" /></a></div>
<div class="MsoNormal">
<b><br /></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The present value of each of
the three payments can be calculated individually, as follows:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="tab-stops: center 3.25in; text-align: center;">
<b><i><span style="font-size: 12pt; line-height: 115%;">The Payment Due at Age 36<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Basic equation:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQHNBhKllFhGR13LWpwJ98q-ZR11jSkuqm29HpTYH8W9O0k8NImlHDf8F2Lt0ScUdqCV8gaYfU1Mi4WZC5thojcyxqIR2cR8qwSoAGcH1XKy0RHmkR-KETmYbhT2uFgQk4dKJImVypwJR0/s1600/present+value+of+a+life+annuity2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQHNBhKllFhGR13LWpwJ98q-ZR11jSkuqm29HpTYH8W9O0k8NImlHDf8F2Lt0ScUdqCV8gaYfU1Mi4WZC5thojcyxqIR2cR8qwSoAGcH1XKy0RHmkR-KETmYbhT2uFgQk4dKJImVypwJR0/s1600/present+value+of+a+life+annuity2.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="tab-stops: center 3.25in; text-align: center;">
<b><i><span style="font-size: 12pt; line-height: 115%;">The Payment Due at Age 37<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Basic equation:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLsKV-hLOI0F8w3Jv7l4cW2Kwus6G5NkIlGVtcuGnV_tv7zir5b4zx9nmdz05g5M-ivVFCVDC7ynFNi_5fcOYencamjaibiDXuAIPOKKea-NQUjJSwhSwKsCRpo11hyphenhyphenM2Xh6kdQDIBkNuz/s1600/present+value+of+a+life+annuity3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLsKV-hLOI0F8w3Jv7l4cW2Kwus6G5NkIlGVtcuGnV_tv7zir5b4zx9nmdz05g5M-ivVFCVDC7ynFNi_5fcOYencamjaibiDXuAIPOKKea-NQUjJSwhSwKsCRpo11hyphenhyphenM2Xh6kdQDIBkNuz/s1600/present+value+of+a+life+annuity3.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="tab-stops: center 3.25in; text-align: center;">
<b><i><span style="font-size: 12pt; line-height: 115%;">The Payment Due at Age 36<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Basic equation:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUizhSSQ8ajTL_MiWnbvoUAFVt4kM6GShf3-WJkQFenlrcQbe3a3dAD_ytrlJJB6mhSCDbD61u0K8Szb0sPmiBpNweqEWWlhKtBqJ0H0Wa2gLi1WtOmCkx5lBV33AUsSuCIJEL-kq-n8Lv/s1600/present+value+of+a+life+annuity4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUizhSSQ8ajTL_MiWnbvoUAFVt4kM6GShf3-WJkQFenlrcQbe3a3dAD_ytrlJJB6mhSCDbD61u0K8Szb0sPmiBpNweqEWWlhKtBqJ0H0Wa2gLi1WtOmCkx5lBV33AUsSuCIJEL-kq-n8Lv/s1600/present+value+of+a+life+annuity4.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The present value at
age 35 of this annuity is the total of these three expressions. The common
multiplier ($100) can be factored out. The fractions to be added together have
a common denominator <span style="font-size: 15px;"><span style="font-family: Verdana, sans-serif;">(</span><span style="font-family: 'Trebuchet MS', sans-serif;">l</span></span><span style="line-height: 17px;"><span style="font-family: Calibri, sans-serif; font-size: xx-small;">35</span></span>). Hence the present
value of the annuity can be expressed as:</div>
<div class="MsoNormal">
<span style="line-height: 21px; text-align: center;"> Present Value = </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhku8SV4QPne7_z5jM08er9rRrdvRQSSXIUQkf2eByqxaz-dvnsiTHf0BBsTuayMKxcWnbsGb7YKjTFl45t7U4ZIabgqMXysMjHDY3ahemAy0uVoOBrY6eybAd2l3Mmx5Aiui5gGSQsM_2R/s1600/present+value+of+a+life+annuity5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhku8SV4QPne7_z5jM08er9rRrdvRQSSXIUQkf2eByqxaz-dvnsiTHf0BBsTuayMKxcWnbsGb7YKjTFl45t7U4ZIabgqMXysMjHDY3ahemAy0uVoOBrY6eybAd2l3Mmx5Aiui5gGSQsM_2R/s1600/present+value+of+a+life+annuity5.PNG" /></a></div>
<div align="center" class="MsoNormal" style="tab-stops: center 3.25in; text-align: center;">
<br /></div>
<div class="MsoNormal">
The numerator of this
expression represents the total to be paid out to the survivors at each age,
with each such amount being discounted at interest to the evaluation date. The
denominator represents the number of persons alive on the evaluation date,
among whom this total present value to be paid in must be allocated.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
If, for example, given
table and 3% interest were used, the present value of the annuity would be
calculated as follows:<o:p></o:p><br />
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 145.05pt;" valign="top" width="193"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="line-height: 17px;"><span style="font-family: Georgia, 'Times New Roman', serif;"><span style="font-size: 15px;">l</span><span style="font-size: xx-small;">x</span></span></span></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 145.05pt;" valign="top" width="193"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>35<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9373807<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 145.05pt;" valign="top" width="193"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>36<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9350279<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 145.05pt;" valign="top" width="193"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>37<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9325594<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 145.05pt;" valign="top" width="193"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>38<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9299482<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjovW2sxDqt6wIZ1XJHXyRuhr6Ob7aiYs8gZoMdFtYDqMiMRqRKFDLdpf8rdAQVFaFFhf_fhYJmT-Ya_X-EquJlvlCbalRkCqHUwGeBin-AcjOSobLmCV-vSFdE9wTrisvcFZxeDbZIqyuv/s1600/present+value+of+a+life+annuity6.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjovW2sxDqt6wIZ1XJHXyRuhr6Ob7aiYs8gZoMdFtYDqMiMRqRKFDLdpf8rdAQVFaFFhf_fhYJmT-Ya_X-EquJlvlCbalRkCqHUwGeBin-AcjOSobLmCV-vSFdE9wTrisvcFZxeDbZIqyuv/s1600/present+value+of+a+life+annuity6.PNG" /></a></div>
<br />
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>n<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqH8GFDUdzQ97BvY4JavFJAU5FmchFeJVCWw8ow2TdFUzLRNH6yoS7lKVBfIlU01mRshdRDHdOZfVa_eM8zKKaIpsglxg1R2uLxE9ypFV_M3D71UnFZFYbJ46EYeg3lQ7i59EsDUXBHaFM/s1600/present+value+of+a+life+annuity8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqH8GFDUdzQ97BvY4JavFJAU5FmchFeJVCWw8ow2TdFUzLRNH6yoS7lKVBfIlU01mRshdRDHdOZfVa_eM8zKKaIpsglxg1R2uLxE9ypFV_M3D71UnFZFYbJ46EYeg3lQ7i59EsDUXBHaFM/s1600/present+value+of+a+life+annuity8.PNG" /></a>
</div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>1<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.970874<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>2<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.942596<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>3<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.915142<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>4<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.888487<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div align="center" class="MsoNormal" style="tab-stops: center 3.25in; text-align: center;">
<br /></div>
<div class="MsoNormal">
From above:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqgXRyTZDVIWBIHUxZLWuCFcwSE0CpLfzgl4xk2aQtXjXhzX8jDBhSrZXfnfIcmF5Jtz5f9_fA8mlglEAvGhwLOgtjCjBjpB7dRIu6aI-DHpxhQA_Fw9xJvCp4RgZD5y-fYVZbpJWO0aYT/s1600/present+value+of+a+life+annuity7.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqgXRyTZDVIWBIHUxZLWuCFcwSE0CpLfzgl4xk2aQtXjXhzX8jDBhSrZXfnfIcmF5Jtz5f9_fA8mlglEAvGhwLOgtjCjBjpB7dRIu6aI-DHpxhQA_Fw9xJvCp4RgZD5y-fYVZbpJWO0aYT/s1600/present+value+of+a+life+annuity7.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">To Illustrate</span></i></b>: Using the given table
and 6% interest, calculate the present value at age 45 of a life annuity of $30
per year for four years, first payment due at age 46.<o:p></o:p><br />
<br /></div>
<div align="center">
<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 135.45pt;" valign="top" width="181"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: Georgia, 'Times New Roman', serif; font-size: 11pt; line-height: 115%;">l</span><span style="font-family: Georgia, 'Times New Roman', serif; font-size: xx-small; line-height: 115%;">x</span></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 135.45pt;" valign="top" width="181"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>45<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9048999<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 135.45pt;" valign="top" width="181"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>46<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9000587<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 135.45pt;" valign="top" width="181"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>47<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8948114<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 135.45pt;" valign="top" width="181"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>48<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8891204<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 135.45pt;" valign="top" width="181"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>49<o:p></o:p></b></div>
</td>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8829410<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
Values of<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqH8GFDUdzQ97BvY4JavFJAU5FmchFeJVCWw8ow2TdFUzLRNH6yoS7lKVBfIlU01mRshdRDHdOZfVa_eM8zKKaIpsglxg1R2uLxE9ypFV_M3D71UnFZFYbJ46EYeg3lQ7i59EsDUXBHaFM/s1600/present+value+of+a+life+annuity8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqH8GFDUdzQ97BvY4JavFJAU5FmchFeJVCWw8ow2TdFUzLRNH6yoS7lKVBfIlU01mRshdRDHdOZfVa_eM8zKKaIpsglxg1R2uLxE9ypFV_M3D71UnFZFYbJ46EYeg3lQ7i59EsDUXBHaFM/s1600/present+value+of+a+life+annuity8.PNG" /></a> are as follows:<br />
<br />
<o:p></o:p></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>n<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqH8GFDUdzQ97BvY4JavFJAU5FmchFeJVCWw8ow2TdFUzLRNH6yoS7lKVBfIlU01mRshdRDHdOZfVa_eM8zKKaIpsglxg1R2uLxE9ypFV_M3D71UnFZFYbJ46EYeg3lQ7i59EsDUXBHaFM/s1600/present+value+of+a+life+annuity8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqH8GFDUdzQ97BvY4JavFJAU5FmchFeJVCWw8ow2TdFUzLRNH6yoS7lKVBfIlU01mRshdRDHdOZfVa_eM8zKKaIpsglxg1R2uLxE9ypFV_M3D71UnFZFYbJ46EYeg3lQ7i59EsDUXBHaFM/s1600/present+value+of+a+life+annuity8.PNG" /></a>
</div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>1<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.943396<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>2<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.889996<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>3<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.839619<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>4<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 135.0pt;" valign="top" width="180"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0.792094<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">Solution:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
The line diagram for
this life annuity appears as follows:<o:p></o:p><br />
<br />
<br /></div>
<div class="MsoNormal">
<span style="height: 15px; margin-left: 367px; margin-top: 31px; position: absolute; width: 2px; z-index: 251666432;"><img height="15" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image034.gif" v:shapes="_x0000_s1034" width="2" /></span><b> $30 $30 $30 $30</b></div>
<div class="MsoNormal">
<span style="position: relative; z-index: 251663360;"><span style="height: 15px; left: 114px; position: absolute; top: -1px; width: 2px;"><img height="15" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image034.gif" v:shapes="_x0000_s1031" width="2" /></span></span><span style="position: relative; z-index: 251665408;"><span style="height: 15px; left: 276px; position: absolute; top: -1px; width: 2px;"><img height="15" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image034.gif" v:shapes="_x0000_s1033" width="2" /></span></span><span style="position: relative; z-index: 251664384;"><span style="height: 15px; left: 193px; position: absolute; top: -2px; width: 2px;"><img height="15" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image034.gif" v:shapes="_x0000_s1032" width="2" /></span></span><span style="height: 3px; margin-left: 40px; margin-top: 4px; position: absolute; width: 329px; z-index: 251662336;"><img height="3" src="file:///C:/Users/Xone/AppData/Local/Temp/msohtmlclip1/01/clip_image035.gif" v:shapes="_x0000_s1030" width="329" /></span><b>Age 45</b><b> * </b><b> </b><br />
<b> </b></div>
<div class="MsoNormal">
<b> 46 47 48 49<o:p></o:p></b><br />
<b><br /></b><br />
<b><br /></b></div>
<div class="MsoNormal">
The expression
for the present value will have a numerator representing the total to be paid
out to the survivors at each age, with each such amount being discounted at
interest to the evaluation date:<o:p></o:p><br />
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhngIAEQrt2bBFodnHgdox1aCMoKCsMoyy1-P55eoN-JFrH5NVhvkpPxvpDXhqObwadqjJM-wZXvdTVvg7qYkgTOsFEffmD_971gv7RjRUWKBZwXsbf0trijMy02Pr5881XyAnKxZOPeQ5e/s1600/present+value+of+a+life+annuity9.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhngIAEQrt2bBFodnHgdox1aCMoKCsMoyy1-P55eoN-JFrH5NVhvkpPxvpDXhqObwadqjJM-wZXvdTVvg7qYkgTOsFEffmD_971gv7RjRUWKBZwXsbf0trijMy02Pr5881XyAnKxZOPeQ5e/s1600/present+value+of+a+life+annuity9.PNG" /></a></div>
<br />
<br />
<br /></div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com2tag:blogger.com,1999:blog-6716798511517720994.post-39044014673552223002012-04-19T17:45:00.000-07:002012-04-19T17:45:18.304-07:00LIFE ANNUITIES<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">In this topic, you will begin to learn how life insurance
companies make important calculations which combine the principles of compound
interest and probability. In a life insurance company, annuity contracts
represent payments being made only if a person is alive, while life insurance
contracts represent payments being made only when a person dies. We will
explain how to calculate the present value and the accumulated value of life
annuity payments, that is, payments which are contingent on a designated person
being alive.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Present and accumulated values for life annuities can be
calculated in a manner quite similar to the method for annuities. We will begin
by considering the present value and accumulated value of a single payment.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"></span></div>
<a name='more'></a><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;">PAYMENT WITH BENEFIT OF
SURVIVORSHIP:<o:p></o:p></span></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></span></i></b></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Asking the question: “How much should a person now age 25
pay for the right to receive $100 at age 50 if that person is then alive to
receive it?”<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">This is the same thing as asking:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">“What is the present value to a person now age 25 of $100
payable at age 50, calculated with the benefit of survivorship?”<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">The phrase <i>with
benefit of survivorship</i> is used to distinguish this situation from one
where only rates of interest are involved. If only rates of interest were
involved in finding the present value, the answer would be:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Basic equation for present value”<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgOZtFHbk3W-PXxXhg_NlSkNGcGQAoH-pOYuwtICzoFb0qRUWwlearhwkGRAbWBl_Hu64gmog_6Jr947A4bbSDSC8LglFmlt5G7HHZidBrdrTr9mhxt-DTw-nM2rO5nhjkch5ElngGczl3/s1600/life+annuities.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgOZtFHbk3W-PXxXhg_NlSkNGcGQAoH-pOYuwtICzoFb0qRUWwlearhwkGRAbWBl_Hu64gmog_6Jr947A4bbSDSC8LglFmlt5G7HHZidBrdrTr9mhxt-DTw-nM2rO5nhjkch5ElngGczl3/s1600/life+annuities.PNG" /></a>
</span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">But now the element of survivorship is
also involved because the person must survive in order to receive the payment.
Therefore, with benefit of survivorship means that payment will be made only if
the designated payer or recipient is alive at the time the payment is due.</span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">To begin solving the problem posed above,
it is necessary to consult a mortality table.</span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBU9Guka0-uQGi3Mk3LQtGQFqO38Iqfrl86ZUjBmJu09goyHKjsUtTgeeGWVbjYQ8tqW7Sv1NcMYUUs13JmPw_7hnxzJ0bRtViLOGHsjd7acVYTFX2y9zbovtgUXlCnOjOM_kl_nUuemHL/s1600/life+annuities+2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: 'Trebuchet MS', sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBU9Guka0-uQGi3Mk3LQtGQFqO38Iqfrl86ZUjBmJu09goyHKjsUtTgeeGWVbjYQ8tqW7Sv1NcMYUUs13JmPw_7hnxzJ0bRtViLOGHsjd7acVYTFX2y9zbovtgUXlCnOjOM_kl_nUuemHL/s1600/life+annuities+2.PNG" /></span></a></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-size: 12pt;"><span style="font-family: 'Trebuchet MS', sans-serif;">The
money paid in will earn interest over the 25- year period. For this example,
the rate will be assumed to be 5%. The basic equation for finding present value
can be used to show that all the money paid in equals the present value of all
the money to be paid out 25 years later. The amount each pays in can then be
found:<o:p></o:p></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqZssmbKtCyavC5NUIXznde0DhLxUXT1OhCFt4jGRjkp29JbF432488JDP9O_X1qUfVaEe4GjsJYS8BVDyW-k2O39bL0Q_7saDFO70ks_2Jtrssq7zKtkerS31FZ6esjQekOUGrIMll637/s1600/life+annuities+3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: 'Trebuchet MS', sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqZssmbKtCyavC5NUIXznde0DhLxUXT1OhCFt4jGRjkp29JbF432488JDP9O_X1qUfVaEe4GjsJYS8BVDyW-k2O39bL0Q_7saDFO70ks_2Jtrssq7zKtkerS31FZ6esjQekOUGrIMll637/s1600/life+annuities+3.PNG" /></span></a></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<span style="font-size: 11pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;">$29.53
is the amount each person would pay in if all were to receive $100, 25 years
later (dead or alive). The $28.88 payment will benefit of survivorship is
smaller because in that case only those who survive are to receive their $100.</span></span><br />
<div>
<span style="font-size: 11pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></span></div>
<div>
<span style="font-size: 11pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></span></div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com1tag:blogger.com,1999:blog-6716798511517720994.post-11647913594947736052012-04-19T07:53:00.000-07:002012-04-19T07:53:41.618-07:00THE CENSUS OPERATION<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">In any country census is conducted within the frame work
established by registration. Whether a census covered the entire population of
a nation or on the some segments there off, it involve the following step.<o:p></o:p></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"></span><br />
<a name='more'></a><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<u><span style="font-size: 14pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;">PLANNING
AND PREPARATION:<o:p></o:p></span></span></u></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">The extent of planning and preparation for a census depends upon the
information being sought and the funds made available.<o:p></o:p></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">a a)<span style="font-size: 7pt;"> </span>It is necessary at the outset to fix up a date
at which a census to be conducted. This date should avoid periods when many are
away from the home on vacations or when large are engaged in festivities. The
census dates we fixed when mild climate. Dates linked with religious or social
events are avoided.<o:p></o:p></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">b b)<span style="font-size: 7pt;"> </span>Another the important points at the time of
planning is to be considered the form of schedule(questionnaire), the best
procedure for data collection, the most efficient means of tabulation of the
entire of the return schedule and to establish controls so that best possible
coverage with least non-sampling error be made.<o:p></o:p></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">c c) In the
design of census schedule (questionnaire) besides taken into consideration
government and other agencies requirements and recommendation of U.N. to be
kept in mind to enhance international comparability of a generating data.<o:p></o:p></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<i><span style="font-size: 14pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;">PRE-TEST:<o:p></o:p></span></span></i></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">Shortly before the conduct of the
censuses several test counts are under taken in order to look in the
practicability and usefulness of the questions. While designing the
questionnaire the subsequent procedure of processing and tabulation of the
census returns have also to keep in mind. A vital step in planning a census is
to secure complete coverage of the area under study this involves preparation
of maps and other related tools. Language of the questionnaire is yet another
important aspect of census enumeration.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">First census
commission of Pakistan remarked that “if he gives three weeks to conduct census
then I will devote two weeks in planning and designing questionnaire for the
census”. Lastly but not the least training of the field staff and organization
of field operation are yet another step in the operation of census.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-size: 16pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;">GATHERING THE FACTS DATA:<u><o:p></o:p></u></span></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">Census may be conducted on a DE-FACTO basis that is count of the persons
present at the place and time of the count or it may be conducted on a DE-JURE basis that is all persons are counted
according to there usual or normal place of residence.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">De-FACTO system of population census
given an exact population on a particular date until and unless DE-FACTO
population census is conducted in a single day (one night) will give over
enumeration of the population. In earlier DE-FACTO population census were
conducted when population movement was little and people use to line in small
villages, areas or segments. Big metropolitan areas were not there. Usually
DE-FACTO is conducted in a single moon lit night because of one day operation
it requires a big army of enumerators. It was difficult in this system to count
moving population. This system was in used up to early 20<sup>th</sup>
centaury. Another difficulty with DE-FACTO population is that proper use of
data in planning is not possible. From 1931 series of censuses in system of
census count has generally abundance. In 1975 SINGAPORE and MALAYSIA use this
system.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<span style="font-size: 11pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;">DE-JURE system
of census enumeration calls for counting of person of there usual and normal
place of residence and the enumeration is carried out about 15 days usual place
of residence are specifically spelled out before the conduct of the census.
This system involves fewer enumerators which can be better trained thus
ensuring better coverage and accuracy. One enumerator is assigned a number of
circles/villages when he/she counts people over a period of 2 to 3 weeks time. In
this process some people are counted twice and some are not counted new born
after the visit of enumerator, is not counted where as a death occurring after
the departure of enumerator is counted. However this method is found more
convenient in term of supervision and operation. Hence it is most commonly used
even in DE-JURE system, one night is declared as census night and the data is
taken as part of reference for the census result.</span></span></div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com1tag:blogger.com,1999:blog-6716798511517720994.post-44074042519973973672012-04-19T07:52:00.000-07:002012-04-19T17:46:04.158-07:00DEMOGRAPHY<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Demography is the science of
human population. A Belgian name of ACHILE GLUILLARD first used the term in
1855 when he published his book in FRENCH named “Elements of Human Statistics
or Comparative Demography”. He defines it as the natural and social history of
the human species or the mathematical knowledge of population, of their general
changes and of their physical civil intellectual and moral conditions.
Population analysis is more or less used as synonymous to demography. However
population analysis has more mathematical and numerical analysis. The term
demography has been derived from two Greek words DEMOS meaning to human
population and GRAPHY means to measured. Demography has further defined in
different senses and levels. We have narrowest sense, broadest sense and widest
sense.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"></span></div>
<a name='more'></a><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<u><span style="font-size: 14pt;"><span style="font-family: 'Trebuchet MS', sans-serif;"><b>DEMOGRAPHY
IN NARROWEST SENSE:</b><o:p></o:p></span></span></u></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">In narrowest sense demography is
considered as the formal demography, is concern with size, distribution,
structure and change of population. Size is simply measured through the number
of unit (persons in the population). Distribution refers to the arrangement of
the population in space at a given time that is geographically or among various
types of residential areas or units.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Structure
in its in narrowest sense is the distribution of population among sex and age
grouping and other person characteristics. Change in the growth or decline of
the total population are of its one of the structural units. The components of
change in total population are births, death and migration.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<u><span style="font-size: 14pt;"><span style="font-family: 'Trebuchet MS', sans-serif;"><b>DEMOGRAPHY
IN BRODEST SENSE:</b><o:p></o:p></span></span></u></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Broadest sense demography
includes additional characteristics of unit these include ethnic
characteristic, economical characteristic and social characteristic. Ethnic
characteristic is like legal, nationality and mother tongue into social
characteristic. Other social characteristic are marital status, family status,
place of birth, literacy and education attainments. Economic characteristic
includes employment economic activity, occupation, industry and incomes. Other
characteristic that might encompassed are genetic inheritance, intelligence and
health but the usual sources of demographic data such as censes, seldom deals
with this directly. Further more demography may look beyond the basic personal
unit to such customary social grouping such as families and married couple.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<u><span style="font-size: 14pt;"><span style="font-family: 'Trebuchet MS', sans-serif;"><b>DEMOGRAPHY
IN WIDEST SENSE:</b><o:p></o:p></span></span></u></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Widest sense of demography
extends to applications of its data and findings in number of fields including
the study of problems that are related to demographic process and human
population. These include the pressure of population on resources,
de-population, family limitations, eugenic, assimilation, urban/rural problem,
main problem and the main distribution of income and resource.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Eugenics
is concern with controlling the population both quantitatively and
qualitatively by separating out mentally and physical defective people from the
act of mating and reproducing.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<u><span style="font-size: 14pt;"><span style="font-family: 'Trebuchet MS', sans-serif;"><b>LEVELS
OF DEMOGRAPHICS STUDIES:</b><o:p></o:p></span></span></u></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Demographic or population studies
can be made at different levels extending its spectrum and are known as “Macro
Demography”. However for minute knowledge demographic analysis may be
performing on a smaller area for example, a city, a town, village or a
designated area. Such studies are term as “Micro Demography”.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Macro
studies are generally performed on global, continent, regional, sub regional
and national language. Micro studies are conducted in sub national, provincial,
District, cities, town, villages, or small De-limited area.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Macro
studies are being made under united nation or its allied organization except
national level which are being done by national government in their respective
countries. All member countries of U.N. are supposed to supply their data to
U.N’s various organization.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><u><span style="font-size: 14pt;"><b>SOURCES
OF DEMOGRAPHIC DATA:</b></span></u><o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Demographic analysis and
population studies either in narrower sense or Browder sense required basic
data on person count and counts of various vital events which are available
through various resources. None of the resources are overlapping rather they
are complimentary to each other. How ever, these resources differed to a great
extend and thus the data generating through them is also to be used with care.
There are three different resources through which we obtained basic demographic
data. Additional data is possible through some indirect sources. The three
basic resources are:</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">1. Census</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">2. Sample
survey</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">3. Registration</span></div>
<div class="MsoListParagraphCxSpLast" style="text-indent: -0.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<u><span style="font-size: 14pt;"><span style="font-family: 'Trebuchet MS', sans-serif;"><b>CONCLUSION:</b><o:p></o:p></span></span></u></div>
<span style="font-size: 11pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;">HOUSER and DUNCAN( static an) regard the field
of demography as consisting of a narrower scope, demographic analysis in a
wider scope and population studies in the widest scope. Demographic analysis is
confined to the components of population, variation and change. Population
studies are concerned not only with the population variable but also with
relationship between population changes and the other variables such as social,
economical, political, biological, genetic, and geographical and the like. The
field of population studies is at least as browed as interest in the
determinants and consciences and trends. UN multilingual (demographic
dictionary) demography is the scientific study of primarily with respect to
their size, their structure and their development.</span></span><br />
<div>
<span style="font-size: 11pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></span></div>
<div>
<span style="font-size: 11pt; line-height: 115%;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></span></div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-68170121774014520612012-04-13T15:15:00.000-07:002012-04-18T10:58:58.958-07:00PROBABILITIES OF DYING<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The probability that one of the events will happen is the
total of the probabilities of each individual event happening.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b>(Probability of
living 1 year) + (Probability of Dying Within 1Year) = (Probability of Either
Living or Dying That Year)<o:p></o:p></b></div>
<div class="MsoNormal">
<b><br /></b></div>
<div class="MsoNormal">
Symbols can be substituted for each of the above
expressions, as follows:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Substitute <i>p<sub>x</sub></i>
for (Probability of Living 1 Year)<o:p></o:p></div>
<div class="MsoNormal">
Substitute <i>q<sub>x</sub></i>
for (Probability of Dying within 1 Year)<o:p></o:p></div>
<div class="MsoNormal">
Substitute 1 (certainty) for (Probability of Either Living
or Dying That Year)<o:p></o:p></div>
<div class="MsoNormal">
Consequently, the equation is</div>
<div class="MsoNormal">
</div>
<a name='more'></a><br /><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6rLBi1UT9OWpAg4IGZ_-gJglF3lKtwW0MtmU3BcTa5TkVUEX5TOvjhgsmPhvN-7ERCc7x9xOMAEd8bn4hfifP0B_PoKPjGT9HUBqo2kGfwHQT9LaxR3XMMxt-egwmLshRcjYolW7AOETI/s1600/.1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6rLBi1UT9OWpAg4IGZ_-gJglF3lKtwW0MtmU3BcTa5TkVUEX5TOvjhgsmPhvN-7ERCc7x9xOMAEd8bn4hfifP0B_PoKPjGT9HUBqo2kGfwHQT9LaxR3XMMxt-egwmLshRcjYolW7AOETI/s1600/.1.PNG" /></a>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">To Illustrate:</span></i></b>
Given that <i>p<sub>46</sub></i> = 0.995138,
how many persons age 46 can be expected to die before reaching age 47 out of a
group of 1,000,000?<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Solution:</span></i></b><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></i></b></div>
<div class="MsoNormal">
Basic equation<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl01QPmbVHicYrXUYQHVE75gCMcaXL-PNJU_g7YP2cZpLhwKdXjNXt83wQIV6X86wjVI-v7qYNk5_2FkiOJKhS4ncPk1fPvBeKlRETrBRDgI2iJiUZASPL_88eE5LM9WShj9294DA4hiHQ/s1600/.2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl01QPmbVHicYrXUYQHVE75gCMcaXL-PNJU_g7YP2cZpLhwKdXjNXt83wQIV6X86wjVI-v7qYNk5_2FkiOJKhS4ncPk1fPvBeKlRETrBRDgI2iJiUZASPL_88eE5LM9WShj9294DA4hiHQ/s1600/.2.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Which means that out of 1,000,000 persons
age 46, we can expect 4,862 to die before reaching age 47.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><u><span style="font-size: 16.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">PROBABILITIES OF DYING
WITHIN n YEARS:<o:p></o:p></span></u></b></div>
<div class="MsoNormal">
The probability that a person age <i>x </i>will die within <i>n</i> years or will die before reaching age (x + n) is represented by
the symbol “<i><sub>n</sub>q<sub>x</sub>” </i>that
is, q with subscripts of n preceding and x following. It is read “<b><i>n q x</i></b>”.
An example would be “<b><i><sub>10</sub>q<sub>45</sub>”</i></b> which
is read “<b><i>10 q 45</i></b>”. It means the probability that a person age 45 will
die within the next 10 years, that is, that the person will die before reaching
age 55.<o:p></o:p></div>
<div class="MsoNormal">
The probability that a person age x will
die within n years (<sub>n</sub> q <sub>x</sub>) is found by dividing the
difference between the number living at ages x and (x + n) by the number living
at age x. this is expressed in equation form as:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirfEvNmeQdCO5YF6ruwa_AqcQ5UKS9u6t83s3_-xqUuUXlMjWxdi0XtcHv_kDIeHd_hanZyZeZ9QMGR2DoZmtJsMiUhvqc6kwTUjypVfP8k_a8INeC7jUgRXDXfixSEKyWa9GZ-vMOikZf/s1600/.3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirfEvNmeQdCO5YF6ruwa_AqcQ5UKS9u6t83s3_-xqUuUXlMjWxdi0XtcHv_kDIeHd_hanZyZeZ9QMGR2DoZmtJsMiUhvqc6kwTUjypVfP8k_a8INeC7jUgRXDXfixSEKyWa9GZ-vMOikZf/s1600/.3.PNG" /></a></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 19px; line-height: 21px;"><b><br /></b></span></div>
<div class="MsoNormal">
The numerator equals the number of people
who die between ages x and (x + n) because the number living at age x is
reduced by all those who die in the interval in order to arrive at the number
still living at age (x + n).<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">To Illustrate</span></i></b>:
Using the following portion of a mortality table, calculate the probability
that a person age 35 will die within the next four years.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>l<sub>x</sub><o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>d<sub>x<o:p></o:p></sub></b></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>35<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9827<o:p></o:p></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
13<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>36<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9814<o:p></o:p></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
13<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>37<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9801<o:p></o:p></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
15<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>38<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9786<o:p></o:p></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
16<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>39<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9770<o:p></o:p></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
16<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>40<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9754<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 1.5in;" valign="top" width="144">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
17<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">Solution</span></i></b><b><i><span style="font-size: 14.0pt; line-height: 115%;">:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Basic equation<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6x-MNlXlr8_ze2bdvJea1NKtLTCggvpdfq_BT5EjEpm6Ir7zn62bUuaGrDge2gYgEj_y6Dv2tgKa5aPI52m1SJXfnwFJWde3bEACUjuTJTDwCGwSLnotaszQybgJ-Np9J2LgssKMax1Cd/s1600/.4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6x-MNlXlr8_ze2bdvJea1NKtLTCggvpdfq_BT5EjEpm6Ir7zn62bUuaGrDge2gYgEj_y6Dv2tgKa5aPI52m1SJXfnwFJWde3bEACUjuTJTDwCGwSLnotaszQybgJ-Np9J2LgssKMax1Cd/s1600/.4.PNG" /></a></div>
<div class="MsoNormal">
<span style="font-size: x-small;"><br /></span></div>
<div class="MsoNormal">
Substitute the values from table<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiZPDKRAIthFIhdmqEFAlRJbLS8sKbbPJomJTQC_IKr9XHpHp-KBbH0Htas4JSJ0HEF8wJ_jOVChKpspuGDYUOCjO3jaJYEit3VGARtqPez6qqHji3nQkUUL0hvPYz0UN_mjL6xphWtP6R/s1600/.5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiZPDKRAIthFIhdmqEFAlRJbLS8sKbbPJomJTQC_IKr9XHpHp-KBbH0Htas4JSJ0HEF8wJ_jOVChKpspuGDYUOCjO3jaJYEit3VGARtqPez6qqHji3nQkUUL0hvPYz0UN_mjL6xphWtP6R/s1600/.5.PNG" /></a></div>
<div class="MsoNormal">
<span style="font-size: x-small;"><br /></span></div>
<div class="MsoNormal">
The number in the numerator, 57, is the
number of people who die between ages 35 and 39. It is equal to the total of
the numbers in the <b><i>d<sub>x</sub></i></b> column, beginning with <b><i>d<sub>35</sub> </i></b>and ending
with<b><i>
d<sub>38 </sub><o:p></o:p></i></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">To Illustrate</span></i></b>:
Using the following portion of a mortality table and a six-year setback for
females, calculate how many of 100,000 females age 27 can be expected to die
within ten years.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Female Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>l<sub>x</sub><o:p></o:p></b></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>21<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9647694<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>22<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9630039<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>23<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9612127<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>24<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9593960<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>25<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9575636<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>26<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9557155<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>27<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9538423<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>28<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9519442<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>29<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9500118<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>30<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9480358<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 139.5pt;" valign="top" width="186">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>31<o:p></o:p></b></div>
</td>
<td style="background: silver; border-bottom: solid black 1.0pt; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9460165<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">Solution<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Six years must be subtracted from the ages before using the
table. This means using the table as if calculating the probability of a female
age 21 reaching age 31. The number of years involved, <b><i>n</i></b>, is 10<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Basic equation:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXyss2EEodeh3w7kmL6MF5UWgYUGYiZVuXAiQrTQ-UaDZb1cltg9NwRn12aqeCRt9mHx8PWRNow5FapFtgev2QR1dIRhUll5rQ1w-o1Gx2Al6Eb0jkpn9GHp6myTa5qITfCe_SucFgHWC6/s1600/.6.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXyss2EEodeh3w7kmL6MF5UWgYUGYiZVuXAiQrTQ-UaDZb1cltg9NwRn12aqeCRt9mHx8PWRNow5FapFtgev2QR1dIRhUll5rQ1w-o1Gx2Al6Eb0jkpn9GHp6myTa5qITfCe_SucFgHWC6/s1600/.6.PNG" /></a></div>
<div class="MsoNormal">
<span style="line-height: 18px;"><br /></span></div>
<div class="MsoNormal">
Substitute the values from the table<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzYtVO9olNeyyikRRgZrxDwvlaZpnE1VyQe8Yj9XA4aFddHuag09HHE5DnZkw7TuLTD03MOigT9KTwK7rsIP3NFVoHY_tXod-NiNgx-Un7MFHnZJ-tXErCxeVnByzYqWPBlI2a66MYJ9wS/s1600/.7.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzYtVO9olNeyyikRRgZrxDwvlaZpnE1VyQe8Yj9XA4aFddHuag09HHE5DnZkw7TuLTD03MOigT9KTwK7rsIP3NFVoHY_tXod-NiNgx-Un7MFHnZJ-tXErCxeVnByzYqWPBlI2a66MYJ9wS/s1600/.7.PNG" /></a></div>
<div class="MsoNormal">
<span style="line-height: 18px;"><br /></span></div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-72980455712674183022012-04-13T14:55:00.000-07:002012-04-18T11:03:33.634-07:00PROBABILITIES OF LIVING:<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
The probability that a person age “x” will die in the next
year is represented by the symbol q<sub>x</sub>. The probability that a person
age “x” will live to reach (x + 1) is represented by the symbol “p<sub>x</sub>”.<o:p></o:p></div>
<div class="MsoNormal">
That is. P with a subscript x. it is read <i>“p sub x”</i> or simply <i>“p x”.</i> An example would be p<sub>34</sub> which is read <i>“p sub 34”</i> or <i>“p 34”</i>. It means the probability that a person age 34 will live to
reach age 35, that is, will be alive for at least one whole year.<o:p></o:p></div>
<div class="MsoNormal">
In general terms, it may be said that if the number living
at age (x + 1) is divided by the number living at age x, the result will be the
probability that a person age x will live to reach age (x + 1). In equation
form, this is written as:<o:p></o:p><br />
<br />
<a name='more'></a><br /></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuZDEAWZfwUlWf-fTM5laaayFJaN3qH-ikAbrgJHjrbbq0_RHyeFLt0z9USQJV3OHyjy5-FAegqz3GTk7_HMiQDzutpwmpTqDA-cBzb9u0U-eN220xUgeQMXR6ljIzeISywHpc_tqBhIXW/s1600/9.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuZDEAWZfwUlWf-fTM5laaayFJaN3qH-ikAbrgJHjrbbq0_RHyeFLt0z9USQJV3OHyjy5-FAegqz3GTk7_HMiQDzutpwmpTqDA-cBzb9u0U-eN220xUgeQMXR6ljIzeISywHpc_tqBhIXW/s1600/9.PNG" /></a></div>
<div class="MsoNormal">
<span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">The
result shows that, according to this particular table, the probability that a
person age 20 will live for at least one year is 0.8885.</span></div>
<div class="MsoNormal">
<span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9n05E-NaMKfT8X62kdkH4NefIGZcrlcnsgaL5hBPMg-2ybDI2pelW2g5I7ZhVdgFZ43DIvWWbU-WFe-KjjFiTmVaNkmHQgyZ3jXMjEiu7Gk1JmOp70o32inIOmQtLcK5oO4iITrjr6i7C/s1600/10.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9n05E-NaMKfT8X62kdkH4NefIGZcrlcnsgaL5hBPMg-2ybDI2pelW2g5I7ZhVdgFZ43DIvWWbU-WFe-KjjFiTmVaNkmHQgyZ3jXMjEiu7Gk1JmOp70o32inIOmQtLcK5oO4iITrjr6i7C/s1600/10.PNG" /></a></div>
<div class="MsoNormal">
<span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">The
result shows that, according to this particular table, the probability that a
person age 50 will be live at least one year is 0.9909.</span></div>
<div class="MsoNormal">
<span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<u><span style="font-size: 18pt; line-height: 115%;">PROBABILITIES OF LIVING FOR n YEARS:<o:p></o:p></span></u></div>
<div class="MsoNormal">
The concepts presented above can be extended to include the
probabilities of a person living for any numbers of years, or dying within any
number of years. The probability that a person age x will live at least <i>n</i> more years, or that the person will reach
age (x+ n), is represented by the symbol “<i><sub>n</sub>p<sub>x</sub></i>”
that is, p with subscripts of n preceding and x following. It is read <i>“n p x”.</i> An example would be <i><sub>25</sub>p<sub>40</sub></i> which is
read “<i>15 p 20”.</i> It represents the
probability that a person age 40 will live at least 25 more years, that is,
that the person will reach age 65.<o:p></o:p></div>
<div class="MsoNormal">
The probability that a person age x will live at least <i>n</i> more years (<i><sub>n</sub>p<sub>x</sub></i>) is found by dividing the number living
at age (x + n) by the number living at age <i>x</i>.
In equation form this is written as:<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTkhum0BznPD_dqPtbZm-EicKoWoGMZm3ULIqDeIQwIgETCIMPx8r5_BZuvhE0Mj3-rNyDwtNKptIm5Bj6DA_e8OFxUAI1OsYeZLuV5E6-1eYnKW8DaRrcxAZ-qi3SlZhyphenhyphenXCLtppXMOzAv/s1600/11.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTkhum0BznPD_dqPtbZm-EicKoWoGMZm3ULIqDeIQwIgETCIMPx8r5_BZuvhE0Mj3-rNyDwtNKptIm5Bj6DA_e8OFxUAI1OsYeZLuV5E6-1eYnKW8DaRrcxAZ-qi3SlZhyphenhyphenXCLtppXMOzAv/s1600/11.PNG" /></a></div>
<div class="MsoNormal" style="text-align: left;">
</div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">To Illustrate</span></i></b>:
Using the following portion of a mortality table, calculate the probability
that a person age 24 will live at least six more years.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYRS9rgvIfLf2jujmp_6J8JmNtgO1JIws0ATs7LQx3kJ62l_Drqoh1ZlWRtu_XACRDjFfATyNQhBbL_soXgkZbrAkE57nDr_WEG13hUz86-A__wJbguPTLrqyYd4Loghv4B3ULy3AOY6v9/s1600/12.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYRS9rgvIfLf2jujmp_6J8JmNtgO1JIws0ATs7LQx3kJ62l_Drqoh1ZlWRtu_XACRDjFfATyNQhBbL_soXgkZbrAkE57nDr_WEG13hUz86-A__wJbguPTLrqyYd4Loghv4B3ULy3AOY6v9/s1600/12.PNG" /></a></div>
<div class="MsoNormal" style="text-align: left;">
</div>
<div class="MsoNormal">
The probability that a person age 24 will
live at least six more years is 0.9184.<o:p></o:p></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">To Illustrate:</span></i></b>
using the following portion of a male mortality table and a three-year setback
for females, calculate the probability that a woman age 36 will live to reach
age 40.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="LightShading1" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Male Age (x)<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>l<sub>x</sub><o:p></o:p></b></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>33<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9209<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>34<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9173<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>35<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9135<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>36<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9094<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>37<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9049<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>38<o:p></o:p></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
9001<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>39<o:p></o:p></b></div>
</td>
<td style="background: silver; border: none; mso-background-themecolor: text1; mso-background-themetint: 63; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8948<o:p></o:p></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 85.5pt;" valign="top" width="114"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>40<o:p></o:p></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 81.0pt;" valign="top" width="108"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
8891<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">Solution:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Three years must be subtracted from the ages before using
the table. This means using the table as if calculating the probability of a
male age 33 reaching age 37. The number of years involved, n is 4<o:p></o:p></div>
<div class="MsoNormal">
Basic equation<o:p></o:p></div>
<div class="MsoNormal">
<span style="line-height: 18px;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh52XyJa1XtOgaXLj87cgjbgkRhOzIBTVg7viVxq6GVhQ-_1nuBpmt3847gDaARPCgPFfWtyO9VgQ4UBgb3aQhE552-GqWEg_-QZBTjGT5plrKE-GgxmMSL22cKqt7FqYRnxg5Hn1cGByaI/s1600/13.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh52XyJa1XtOgaXLj87cgjbgkRhOzIBTVg7viVxq6GVhQ-_1nuBpmt3847gDaARPCgPFfWtyO9VgQ4UBgb3aQhE552-GqWEg_-QZBTjGT5plrKE-GgxmMSL22cKqt7FqYRnxg5Hn1cGByaI/s1600/13.PNG" /></a></div>
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<span style="line-height: 18px;"><br /></span></div>
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<br /></div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-65779709222487287552012-04-13T14:39:00.000-07:002012-04-13T14:39:05.739-07:00RATES AND RATIO<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%;"> </span><u><span style="font-size: 18.0pt; line-height: 115%;">RATIO:</span></u></div>
<div class="MsoNormal">
Ratio measures change
in “X” per unit change in”y”.<u><span style="font-size: 18.0pt; line-height: 115%;"><o:p></o:p></span></u></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 12.0pt; line-height: 115%;">Ratio = x/y</span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;line-height:
115%;font-family:"Cambria Math","serif"'><m:r>y</m:r></span></i></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -11.5pt; position: relative; top: 11.5pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><v:stroke joinstyle="miter"><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"><v:f eqn="sum @0 1 0"><v:f eqn="sum 0 0 @1"><v:f eqn="prod @2 1 2"><v:f eqn="prod @3 21600 pixelWidth"><v:f eqn="prod @3 21600 pixelHeight"><v:f eqn="sum @0 0 1"><v:f eqn="prod @6 1 2"><v:f eqn="prod @7 21600 pixelWidth"><v:f eqn="sum @8 21600 0"><v:f eqn="prod @7 21600 pixelHeight"><v:f eqn="sum @10 21600 0"></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas><v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"><o:lock aspectratio="t" v:ext="edit"></o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 27pt; width: 6.75pt;" type="#_x0000_t75"><v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"></v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 14.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal">
There are different types of ratio:<o:p></o:p></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.5in;">
<!--[if !supportLists]-->i)<span style="font-size: 7pt;">
</span><!--[endif]-->When we have numerator and denominator belongs
to the same population.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.5in;">
<!--[if !supportLists]-->ii)<span style="font-size: 7pt;">
</span><!--[endif]-->When we have numerator and denominator belongs
to the different population (universe). We call the ratio as proportion (specific
name of ratio).<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .75in; mso-add-space: auto;">
Proportion<span style="font-size: 14.0pt; line-height: 115%;">= x/x+y</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .75in; mso-add-space: auto;">
Proportion tends is equal to zero if x=0 and proportion is equal
to 1 if y=0.</div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
Ratio indicates the relative magnitude of a numerator and denominator.<o:p></o:p></div>
<div class="MsoNormal">
</div>
<a name='more'></a><br /><br />
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">SEX RATIO:<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .75in; mso-add-space: auto;">
Sex ratio is defined as
the male population and female population presenting in percentages. As:<o:p></o:p></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .75in; mso-add-space: auto;">
<br /></div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%;">R= Male/Female </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span style='font-size:
14.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="p"/></m:rPr>male</m:r></span></m:num><m:den><span
style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="p"/></m:rPr>female</m:r></span></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;line-height:
115%;font-family:"Cambria Math","serif"'><m:r> </m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -10.0pt; position: relative; top: 10.0pt;"><v:shape id="_x0000_i1025" style="height: 27pt; width: 35.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 14.0pt; line-height: 115%;">* 100<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto;">
Sex ratio means male per 100 female. We can calculate different types of
sex ratio.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto;">
<u>Sex ratio of birth:</u> <u><o:p></o:p></u></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.0in; mso-add-space: auto;">
Number of males’ birth per 100
female births. Ratio if less than 100 means more female than male birth. If
ratio=100 same number of male and female birth. If the ratio is greater than
100 means more males than females. In human population there is more male birth
then female birth with ratio generally between 104 and 107.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.0in; mso-add-space: auto;">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">CHILD WOMEN RATIO: <o:p></o:p></span></i></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhL2Mib8Yw00H1BNwtzuC5SjP3GvzcnuP0E53gQVFalLowFSN8LAJozIK9SsJ08divx-uR00YuYhw9whxFcm73m8ua4LgrSxKVdZjXtY8uavvN63NjsRZzoyEwDtNSgp7ExuZ_FV_lCg-n/s1600/8.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhL2Mib8Yw00H1BNwtzuC5SjP3GvzcnuP0E53gQVFalLowFSN8LAJozIK9SsJ08divx-uR00YuYhw9whxFcm73m8ua4LgrSxKVdZjXtY8uavvN63NjsRZzoyEwDtNSgp7ExuZ_FV_lCg-n/s1600/8.PNG" /></a></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .75in; mso-add-space: auto;">
<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto;">
Demographers define some age group and gave different name.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.5in;">
<!--[if !supportLists]-->i)<span style="font-size: 7pt;">
</span><!--[endif]--><u>ADULT:</u> Zero years, for purpose of
classification all babies who have not reached their first birth date.<u><o:p></o:p></u></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.5in;">
<!--[if !supportLists]-->ii)<span style="font-size: 7pt;">
</span><!--[endif]--><u>CHILD: </u>All those children who have not
reach their fifth birth date (0-4) years.<u><o:p></o:p></u></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.5in;">
<!--[if !supportLists]-->iii)<span style="font-size: 7pt;">
</span><!--[endif]--><u>YOUTH: </u>All those children who have not
reach their 15 birthday (5-14) years.<u><o:p></o:p></u></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.5in;">
<!--[if !supportLists]-->iv)<span style="font-size: 7pt;">
</span><!--[endif]--><u>YOUNG:</u> Adults and economically active
working(15-60)<u><o:p></o:p></u></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.5in;">
<!--[if !supportLists]-->v)<span style="font-size: 7pt;">
</span><!--[endif]--><u>OLD AGE OR AGED: </u>Age includes from 60+.
If proportion of old age population start increasing then this type of population
is called ageing population.<u><o:p></o:p></u></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.5in;">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">DEPENDENCY RATIO: <o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Dependency ratio is
observed as;<b><i><span style="font-size: 16.0pt; line-height: 115%;"><o:p></o:p></span></i></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigDp0eUr7i076-dr7nJxGSLZSC27cRwXN6zPTE48N_59zw2ARomiO4R7VfD84jC7AaTK43ZOnVJ3OFx4QEBTP83uzDn2QqiUZYqaS-gvyWTB_VK8Jj594tpAwlOnkDacteEJTDPML4KdLg/s1600/7.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigDp0eUr7i076-dr7nJxGSLZSC27cRwXN6zPTE48N_59zw2ARomiO4R7VfD84jC7AaTK43ZOnVJ3OFx4QEBTP83uzDn2QqiUZYqaS-gvyWTB_VK8Jj594tpAwlOnkDacteEJTDPML4KdLg/s1600/7.PNG" /></a></div>
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<span style="line-height: 18px;"><br /></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">LABOR FORCE
PARTICIPATION:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
It
is not calculated for entire world but for small segment:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
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<span style="line-height: 18px;"><br /></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">TERRITORIAL
DISTRIBUTION RATIO:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
It is defined as the ratio between populations in a segment of territory
to the total population of the country. For example;<o:p></o:p></div>
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<div align="center" class="MsoNormal" style="text-align: center;">
<span style="line-height: 18px;"><br /></span></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">DENSITY OF POPULATION</span></i></b><span style="font-size: 12.0pt; line-height: 115%;">:<o:p></o:p></span></div>
<div class="MsoNormal">
It is the ratio between total populations to the total area to which the
population belongs, for example:<o:p></o:p></div>
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<div class="MsoNormal">
<span style="font-size: 14.0pt; line-height: 115%;"> </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-size:14.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><span style='font-size:
14.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="p"/></m:rPr>Total population of the country</m:r></span></m:num><m:den><span
style='font-size:14.0pt;line-height:115%;font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="p"/></m:rPr>Total area in sq.K.m</m:r></span></m:den></m:f></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><v:shape id="_x0000_i1025" style="height: 29.25pt; width: 150pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\msohtmlclip1\01\clip_image008.png">
</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoNormal">
It shows how densely an area is populated. A low value indicates
sparsely populated area. <o:p></o:p></div>
<div class="MsoNormal">
<u><span style="font-size: 18.0pt; line-height: 115%;"><br /></span></u></div>
<div class="MsoNormal">
<u><span style="font-size: 18.0pt; line-height: 115%;">RATES: <o:p></o:p></span></u></div>
<div class="MsoNormal">
Rate measures the frequency with which an event occurs in a define
population during a given length of time. Rates are special cases of a ratio.
Rates are associated with population changes. Numerator counts of events that
occur during a period. Denominator is a mid point population or person years or
other person time unit of exposure for the same period at the numerator.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">TOTAL FERTILITY RATE:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
ASFR through gives an
indication of fertility behavior in a very logical manner, however, it requires
a grasp of about 7 values. Hence to abbreviate and to arrive at a one single
index ASFR are summed and multiplied by size of age groups of mother (k) to
yield Total Fertility Rate (TFR).<o:p></o:p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCE0xWO03-DpjBPGUbtGauAdNQw1KTqB6CMAptg6Ez7ghGVsmPmOmqi5M6j3Ptz7lTrrIi4z6evlRCLk-QVxlAPZXX53vZPn_drG3xIulA3h8ehM7KnZPdfbwx2mRUQ4Ku42zVxpa3R9nO/s1600/3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCE0xWO03-DpjBPGUbtGauAdNQw1KTqB6CMAptg6Ez7ghGVsmPmOmqi5M6j3Ptz7lTrrIi4z6evlRCLk-QVxlAPZXX53vZPn_drG3xIulA3h8ehM7KnZPdfbwx2mRUQ4Ku42zVxpa3R9nO/s1600/3.PNG" /></a></div>
<div align="center" class="MsoNormal" style="margin-left: 32.25pt; text-align: center;">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">GROSS REPRODUCTION
RATE:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
A mother (female) is going to be replaced by female in future,
therefore, as an index of replacement we must calculate an index taking female
birth only. Hence multiplying the TFR by the ratio of female birth with total
births, yielding a new index known as Gross Reproduction Rate (GRR)<o:p></o:p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgafa3urzz5j3oFk8GpLD_uYJfhRVRp-NF1eYv1DkiPP7SAR8Iv03kT4b0mEnmzdFwtgvvh83pqxzPrWAND6xCZvlxfQdqpVMRoiykqBRRwVbbx9K4DHStkSq6VE-s9GcsLSbj6dkup8Pb/s1600/2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgafa3urzz5j3oFk8GpLD_uYJfhRVRp-NF1eYv1DkiPP7SAR8Iv03kT4b0mEnmzdFwtgvvh83pqxzPrWAND6xCZvlxfQdqpVMRoiykqBRRwVbbx9K4DHStkSq6VE-s9GcsLSbj6dkup8Pb/s1600/2.PNG" /></a></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 19px; line-height: 21px;"><br /></span></div>
<div class="MsoNormal">
Where F: ratio of female births.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12.0pt; line-height: 115%;">NET REPRODUCTION RATE:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
However all female born will not survive to reach the age of their
mothers, hence a further refinement in GRR is made by multiplying it by the
proportion of survival s<sub>i</sub>, the resultant is known as Net
Reproduction Rate (NRR).<o:p></o:p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj-FLzU-JxL4o1pO99VroeLgvwfqcd8887C2DdsHTrVKAEqEWKJrtn_FoQeLiEp-kAUQ-kLr_AVhGe9Pb42CNphjlYlhpSnq5DftaHr9LOzvHwiWUKJR9FIWRVlOBKdQgFuvK0FYDNbm4i/s1600/1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj-FLzU-JxL4o1pO99VroeLgvwfqcd8887C2DdsHTrVKAEqEWKJrtn_FoQeLiEp-kAUQ-kLr_AVhGe9Pb42CNphjlYlhpSnq5DftaHr9LOzvHwiWUKJR9FIWRVlOBKdQgFuvK0FYDNbm4i/s1600/1.PNG" /></a></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 19px; line-height: 21px;"><br /></span></div>
<div class="MsoNormal">
Where s<sub>i</sub>: survival proportion
of female and birth to age of their mothers. This can be found from l<sub>x</sub>
column of life table s<sub>i</sub> = l<sub>i</sub>/l<sub>0</sub>.<o:p></o:p></div>
<i><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">Generally TFR > GRR > NRR and the ratio
between them is around 50%.</span></i></div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com2tag:blogger.com,1999:blog-6716798511517720994.post-32415646347033036272012-04-13T14:13:00.000-07:002012-04-13T14:13:16.200-07:00MORTALITY & FERTILITY<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
<div class="MsoNormal">
<u><span style="font-size: 16.0pt; line-height: 115%;">MORTALITY:<o:p></o:p></span></u></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt;">Mortality
rate (word mortality comes from mortal, which originates from Latin Mors, means
death) is the number of deaths (from a dieses or in general).Per thousand
people and typically reported on an annually basis. It is distinct from
mortality rate, which refers to the no of people who have a dieses compared to
the total no of people in a population. The United Nations and World Health
Organization have proposed following definition of death or mortality.<o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-size: 12.0pt;">“The mortality rate is the ratio of the
number of deaths during a given time period per 100,000 live births during the
same period of time”.</span></i><span style="font-size: 12.0pt;"><o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-size: 12.0pt;"></span></i></div>
<a name='more'></a><i><br /></i><br />
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</div>
<div class="MsoNormal">
<b><i><span style="font-size: 16.0pt; line-height: 115%;">CRUDE DEATH RATE:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Mortality study is made through the statistics of deaths
occurring during a calendar year and mid year population i.e. population as on
1<sup>st</sup> July of the year.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%;">Crude death rate: C.D.R = </span><span style="font-family: Calibri, sans-serif;"><span style="font-size: 15px; line-height: 17px;">D/P</span></span><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> * 100</span><span style="font-size: 14.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i>D=Number of deaths
during a calendar year.<o:p></o:p></i></div>
<div class="MsoNormal">
<i>P=Population as on 1<sup>st</sup>
July of the year.<o:p></o:p></i></div>
<div class="MsoNormal">
It expresses number of deaths per 1000 persons per year.<o:p></o:p></div>
<div class="MsoNormal">
C.D.R is the simplest way of expressing force of
mortality. However, it fails to
distinguish between population having different age structures.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 16.0pt; line-height: 115%;">INFANT MORTALITY RATE:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
Infants are defined as babies who have not reached their
first birth day. In terms of age they are grouped as ‘O’ year old. Infant
mortality rate is defined as the ratio of number of infants deaths during a
calendar year with the total number of births recorded in the same year.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%;">I.M.R = </span><span style="font-family: Calibri, sans-serif;"><span style="font-size: 15px; line-height: 17px;">Do/B</span></span><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> * 100</span><span style="font-size: 14.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></div>
<div class="MsoNormal">
<i>D<sub>0</sub>=Infants
deaths during a calendar year<o:p></o:p></i></div>
<div class="MsoNormal">
<i>B=number of live
births registered during the same calendar year.</i><o:p></o:p></div>
<div class="MsoNormal">
There are some
patent errors present in the IMR. First types of errors are due to definitional
difficulty between a “Live birth” and “Still birth”. Some babies born live but
dying within few seconds after birth are classified as ‘Still born’. Second types
of errors are due to the fact that babies born last year remain infants in the
first six months of the current year
,similarly babies born in the current year will remain Infants unto first six
months of the coming year. Hence the cohort of Infants born (denominator) does
not match properly. Simplest among them is to take data for 3 consecutive year
and then to find its averages.<o:p></o:p></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="line-height: 18px;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWBX6Nh-yrhXhKuwRykEm0R4QH3jJiQqsyqrTMH9bLCR1HtXo1WictyGC1qIZpudQsqK-kEOvv2We9EKdNk_-YPTptb0Q4z62agEXSSH8fkY-XvDa_danX_d21dQPSSZ2oUZ3u_EzAkZQo/s1600/Capture5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWBX6Nh-yrhXhKuwRykEm0R4QH3jJiQqsyqrTMH9bLCR1HtXo1WictyGC1qIZpudQsqK-kEOvv2We9EKdNk_-YPTptb0Q4z62agEXSSH8fkY-XvDa_danX_d21dQPSSZ2oUZ3u_EzAkZQo/s1600/Capture5.PNG" /></a></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="line-height: 18px;"><br /></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 16.0pt; line-height: 115%;">SPECIFIC DEATH RATES:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
It has been remarked
earlier that crude death rates does not take into account the age distribution
of the population and thus creates errors in its interpretation, therefore
specific death rates are calculated .Most common specific death rates are
<o:p></o:p></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 50.25pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->1)<span style="font-size: 7pt;">
</span><!--[endif]-->Age and sex specific death rates. <o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 50.25pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->2)<span style="font-size: 7pt;">
</span><!--[endif]-->Case Fatality Death rates.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 50.25pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->3)<span style="font-size: 7pt;">
</span><!--[endif]-->Death rates by occupation or Socio Economic
Status.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 50.25pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->4)<span style="font-size: 7pt;">
</span><!--[endif]-->Maternal Mortality Rate.<o:p></o:p></div>
<div class="MsoNormal" style="margin-left: 32.25pt;">
For age sex specific death Rate (ASSDR) we
require data of death and mid year population by age and sex groups. Numbers of
Deaths in each group are divided by respective mid year population. The ASDR
follow a specific curve as shown in graph:<o:p></o:p></div>
<div class="MsoNormal" style="margin-left: 32.25pt;">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
Ages (i)<o:p></o:p></div>
</td>
<td nowrap="" style="border-left: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
Population (Pi)<o:p></o:p></div>
</td>
<td nowrap="" style="border-left: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
Deaths (Di)<o:p></o:p></div>
</td>
<td nowrap="" style="border-left: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
ASDR = mi=
(Di/Pi)*1000<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0 - 14<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
16837000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
288000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
17.11<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
15 - 24<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
6737000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
19000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
2.82<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
25 - 39<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
8053000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
21000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
2.61<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
40 - 54<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
4848000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
33500<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
6.91<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
55 - 69<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
2316000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
38300<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
16.54<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
70 - 84<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
961000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
56700<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
59.00<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 48.8pt;" valign="top" width="65">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
85+<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
172000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 61.8pt;" valign="top" width="82">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
15000<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 117.8pt;" valign="top" width="157">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; margin-left: 32.25pt; margin-right: 0in; margin-top: 0in;">
87.21<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal" style="margin-left: 32.25pt;">
<br /></div>
<div class="MsoNormal" style="margin-left: 32.25pt;">
<br /></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKagjHw58ww16tFsh04xYckaP2X_s4tRI5lBpF9CllHvMuo8f7MFYF2zYWM7AJpZ3pF2kqzSTYmHwe3FII5DtlgOhrlmetdH7KPuKJqacS2BHHlF5fnv8_xj0UJ737tWCvNQPe534oETtX/s1600/Capture3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKagjHw58ww16tFsh04xYckaP2X_s4tRI5lBpF9CllHvMuo8f7MFYF2zYWM7AJpZ3pF2kqzSTYmHwe3FII5DtlgOhrlmetdH7KPuKJqacS2BHHlF5fnv8_xj0UJ737tWCvNQPe534oETtX/s1600/Capture3.PNG" /></a><br />
<div class="MsoNormal" style="margin-left: 32.25pt;">
<br /></div>
<div class="MsoNormal" style="margin-left: 32.25pt;">
<br /></div>
<div class="MsoNormal">
<u><span style="font-size: 18.0pt; line-height: 115%;">FERTILITY:<o:p></o:p></span></u></div>
<div class="MsoNormal">
Fertility in contrast
to mortality is studied through the frequency of number of live births during
calendar year in any population.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 16.0pt; line-height: 115%;">CRUDE BIRTH RATE:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
The first basic
index measuring Fertility is Crude Birth Rate (CBR). It is defined as the ratio
of number of live births recorded in a calendar year to the mid year population
of that calendar year. <o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%;">C.B.R = B/P </span><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">* 1000</span><span style="font-size: 14.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
C.B.R is a
comparable index to C.D.R However, its own definition suffers form a serious
draw back .All person in denominator P are not exposed to the risk of giving births . Hence numerator do not
match together, whereas this defect is not present in CBR and CDR serves the
purpose of finding rate of natural increase as the difference between them .</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<o:p></o:p></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%;">Rate of natural Increase =CBR-CDR.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 16.0pt; line-height: 115%;">GENERAL FERTILITY RATE (GFR):<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
AS a refinement to
CBR a General Fertility Rate (GRF) is calculated in which denominator is mid
year female population of the age group 15-49. The age group 15-49 for females
is known as fertile age group, as almost all births takes places within this age
group. <o:p></o:p></div>
<div class="MsoNormal">
Hence <o:p></o:p></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBTQ2imY1OTIAEn-6FIUQsWTtYuTIMG0Q1Isrxqkg_ZQpJED19ZDJOvH4iAkMLtQBW50MQtTxyaIM2eRKbIE58JVjppGMQeib1uo_kbBqSM0iN9kzp39cs_cAnpwvuTQZzmAr0IbZzw-Z3/s1600/Capture2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBTQ2imY1OTIAEn-6FIUQsWTtYuTIMG0Q1Isrxqkg_ZQpJED19ZDJOvH4iAkMLtQBW50MQtTxyaIM2eRKbIE58JVjppGMQeib1uo_kbBqSM0iN9kzp39cs_cAnpwvuTQZzmAr0IbZzw-Z3/s1600/Capture2.PNG" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-size: 16.0pt; line-height: 115%;">AGE SPECIFIC FERTILITY
RATES:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
As a more in-depth
study of behavior of fertility in human population Age Specific Fertility rates
are found with respect to ages of mothers, usually in five year age groupings 15-19.20-24…
up to 45-49 for mothers. The pattern of ASFR is usually a bell shaped curve.
Table shows the working of calculation of ASFR <o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
Age of mothers<o:p></o:p></div>
</td>
<td nowrap="" style="border-left: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
Fi (Female Population)<o:p></o:p></div>
</td>
<td nowrap="" style="border-left: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
Bi<o:p></o:p></div>
</td>
<td nowrap="" style="border-left: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
ASFR= (Bi/Fi)<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
15 - 19<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
850589<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
59537<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0.069995<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
20 -24<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
784307<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
197023<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0.251206<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
25 - 29<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
611847<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
181782<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0.297104<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
30 - 34<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
505115<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
120764<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0.239082<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
35 - 39<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
445275<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
77301<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0.173603<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
40 - 44<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
367449<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
38252<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0.104102<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
45 - 49<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
297879<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
13044<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
0.043790<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 8; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 79.8pt;" valign="top" width="106">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
Total<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 113.8pt;" valign="top" width="152">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
3862461<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 54.8pt;" valign="top" width="73">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
687703<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 15.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 65.8pt;" valign="top" width="88">
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
1.178881<o:p></o:p></div>
</td>
</tr>
</tbody></table>
</div>
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<o:p> </o:p>ASFR can also be calculated for various subgroup of
population, e.g., married, unmarried, ethnic groups, working women etc.</div>
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<o:p></o:p></div>
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<br /></div>
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<b><i><span style="font-size: 16.0pt; line-height: 115%;">TOTAL FERTILITY RATE:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
ASFR through gives an
indication of fertility behavior in a very logical manner, however, it requires
a grasp of about 7 values. Hence to abbreviate and to arrive at a one single
index ASFR are summed and multiplied by size of age groups of mother (k) to
yield Total Fertility Rate (TFR).</div>
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<br /></div>
<br />
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com2tag:blogger.com,1999:blog-6716798511517720994.post-5687001905104736772012-04-13T13:11:00.001-07:002012-04-13T13:15:10.758-07:00LIFE TABLE<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
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<span style="font-size: 12pt;">A
life table presents a set of tabulation that describes the probability of
dying, the death rate, and the number of survivals for each age or age group. Accordingly,
life expectancy is at word is an outward of a life table. <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-size: 12pt;">In actuarial
science a life table (also called the mortality table or actuarial table) is a
table which shows for a person at each age, what is the probability is that
they die before their next birthday. From this starting point, a no of
statistics can be derived and also included in the table.<o:p></o:p></span></div>
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<span style="font-size: 12pt;"></span></div>
<a name='more'></a><br />
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<div style="text-align: left;">
<span style="font-size: 12pt;"><br /></span></div>
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<div class="MsoListParagraphCxSpFirst" style="margin-left: 0.75in; text-indent: -0.5in;">
<div style="text-align: left;">
<span style="font-size: 14pt;">i)<span style="font-size: 7pt;"> </span></span><span style="font-size: 12pt;">The probability
of serving any particular year of age.</span><span style="font-size: 14pt;"><o:p></o:p></span></div>
</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
<div style="text-align: left;">
<span style="font-size: 14pt;">ii)<span style="font-size: 7pt;">
</span></span><span style="font-size: 12pt;">Reaming life
expectancy for people at different ages.</span></div>
</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
<div style="text-align: left;">
<span style="font-size: 19px;">iii) </span><span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;">The proportion of the original work COHORT is
also still alive.</span></div>
</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%; text-indent: -0.5in;"><br /></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%; text-indent: -0.5in;">Life tables are usually constructed separately
for men and for women because of their ubstantially </span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;">different mortality rate.
Other characteristics can also be used to distinguish different risk, such as </span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;">smoking status, occupation, soco-economic class and other class.</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; text-indent: -0.5in;">
</div>
<div class="MsoNormal">
<b><u><span style="font-size: 16pt;">KINDS OF LIFE TABLE: </span></u></b></div>
<div class="MsoNormal">
<span style="font-size: 12pt; text-indent: -0.5in;">There are two classic forms of life table,</span></div>
<div class="MsoNormal">
<span style="font-size: 12pt; text-indent: -0.5in;"><br /></span></div>
<div class="MsoNormal">
<span style="font-size: 12pt; text-indent: -0.5in;">i)</span><span style="font-size: 14pt; text-indent: -0.5in;"><span style="font-size: 7pt;"> </span></span><span style="font-size: 12pt; text-indent: -0.5in;">Cohort (or
generation)</span></div>
<div class="MsoNormal">
<span style="font-size: 12pt; text-indent: -0.5in;">ii) </span><span style="font-size: 12pt; text-indent: -0.5in;">Current (or
period table)</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1in; text-indent: -0.25in;">
<span style="font-size: 12pt;">a)<span style="font-size: 7pt;"> </span></span><span style="font-size: 12pt;">Complete life table and</span><span style="font-size: 14pt;"><o:p></o:p></span></div>
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"> b) A bridged life table.</span><br />
<div class="MsoListParagraph" style="margin-left: 0.75in; text-indent: -0.5in;">
<span style="font-size: 14pt;"><o:p></o:p></span></div>
<br />
<br />
<br />
<div>
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"><br /></span></div>
<div>
<b><i><span style="font-family: Calibri, sans-serif; font-size: 16pt; line-height: 115%;">COHORT
LIFE TABLE:</span></i></b></div>
<div>
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;">Cohort
life tables consist of monitoring a population longitudinally from a determine
event. (For example: a birth cohort or a treatment cohort in a clinical trial)
until all the individuals die or until the observation period is discontinued.
The cohort table is usually used in the survival analysis of clinical trials,
which are carried out on a smaller population sample and over a short period of
time.</span></div>
<div>
<b><i><span style="font-family: Calibri, sans-serif; font-size: 16pt; line-height: 115%;"><br /></span></i></b></div>
<div>
<b><i><span style="font-family: Calibri, sans-serif; font-size: 16pt; line-height: 115%;">CURRENT
LIFE TABLE:</span></i></b></div>
<div>
<span style="font-size: 12pt;">Current life tables
provide a transversal view of mortality and survival expectancies at all ages
of a population during a short period of time, usually a year. They depend
directly on age specific mortality rates for the year for which they are
constructed.</span></div>
<div>
<span style="font-size: 12pt;"><br /></span></div>
<div>
<span style="font-size: 16pt; text-indent: -0.25in;">a)<span style="font-size: 7pt;">
</span></span><u style="text-indent: -0.25in;"><span style="font-size: 16pt;">COMPLETE LIFE TABLE OR UNABRIDGED LIFE TABLE:</span></u></div>
<div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt;"> The complete life
table is constructed using single year of age from birth to the applicable age.</span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 16pt; text-indent: -0.25in;">b)<span style="font-size: 7pt;">
</span></span><u style="text-indent: -0.25in;"><span style="font-size: 16pt;">ABRIDGE LIFE TABLE:</span></u></div>
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"> However, the
abbreviated (abridge) life table are more often used. In which each age is
presented in groups, usually of children under one year, children one to four
years and five year age groups for the remainder of the ages until the final
age interval which remains open.</span></div>
<div>
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"><br /></span></div>
<div>
<div class="MsoListParagraphCxSpFirst">
<b><u><span style="font-size: 16pt;">COMPARISION
BETWEEN COMPLETE AND ABRIDGE LIFE TABLE:<o:p></o:p></span></u></b></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt;"> <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-size: 12pt;"> There are small
differences in life tables measures derived from averaged and complete life
table. Abridge life table used group data or group age data and open ended
upper age group. By comparison, complete life tables use single year of age
data.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-size: 12pt;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraphCxSpFirst">
<b><u><span style="font-size: 16pt;">ASSUMPTIONS
OF LIFE TABLE:<o:p></o:p></span></u></b></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1in; text-indent: -0.5in;">
<span style="font-size: 18pt;">i)<span style="font-size: 7pt;">
</span></span><span style="font-size: 12pt;">The cohort is
closed.</span><span style="font-size: 18pt;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1in; text-indent: -0.5in;">
<span style="font-size: 18pt;">ii)<span style="font-size: 7pt;">
</span></span><span style="font-size: 12pt;">A person dies
according to fix schedule.</span><span style="font-size: 18pt;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1in; text-indent: -0.5in;">
<span style="font-size: 18pt;">iii)<span style="font-size: 7pt;">
</span></span><span style="font-size: 12pt;">Cohort starts
from some standards number. Known as Radix (like suppose no of hundred
thousand).</span><span style="font-size: 18pt;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1in; text-indent: -0.5in;">
<span style="font-size: 18pt;">iv)<span style="font-size: 7pt;">
</span></span><span style="font-size: 12pt;">At each age
(generally deaths are evenly spare over time). </span><span style="font-size: 18pt;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpLast">
<b><u><span style="font-size: 16pt; line-height: 115%;"> COLUMNS OF LIFE TABLE:<o:p></o:p></span></u></b></div>
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;">Life table is a
compact from of showing mortality pattern of a cohort of population. Usually it
contains 8 columns as shown below:</span><br />
<div class="MsoListParagraphCxSpLast">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy8ZfDuHvTsB1OmZ2HrPf9rm4HUP95nhtKKbkyT9rXhtFJTSjtscyPcKKbt8hcIjdu0ew_NFdnKOht05ni4m-fS0FcMqkHT_Y-5_A1-nz-L5-qJQuY2x2ZLzaVnYY7f5c_fa7tdhPVHulQ/s1600/Capture+4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy8ZfDuHvTsB1OmZ2HrPf9rm4HUP95nhtKKbkyT9rXhtFJTSjtscyPcKKbt8hcIjdu0ew_NFdnKOht05ni4m-fS0FcMqkHT_Y-5_A1-nz-L5-qJQuY2x2ZLzaVnYY7f5c_fa7tdhPVHulQ/s1600/Capture+4.PNG" /></a></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraphCxSpFirst">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN#1:</span></i></b></div>
<div class="MsoListParagraphCxSpFirst">
<span style="font-size: 12pt; line-height: 115%;">Column 1
of ages is representing by x. Ages are either taken in a single year as 0, 1-4,
5-9 … Age zero signifies infants, those who have not reached first birthday of
their life.</span></div>
<div class="MsoListParagraphCxSpFirst">
<span style="font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN#2:<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">The Column 2 represents age specific
death rate signified by m<sub>x. </sub>They are calculated from population of
the calendar year for which data has been collected, using classical definitions
ratio of deaths in a year to mid-year population.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;"> l<sub>x</sub> = P<sub>x</sub> + </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; top: 9pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 5.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_CCA39032-DD88-4E3C-AB2C-AFB10AB48D53.0\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><span style="font-size: 12pt; line-height: 115%;"> d<sub>x</sub><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">Or P<sub>x</sub> = l<sub>x</sub> - </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; top: 9pt;"><v:shape id="_x0000_i1025" style="height: 22.5pt; width: 5.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_CCA39032-DD88-4E3C-AB2C-AFB10AB48D53.0\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><span style="font-size: 12pt; line-height: 115%;"> d<sub>x<o:p></o:p></sub></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">Where;<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;"> P<sub>x</sub> = mid year population.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;"> l<sub>x</sub> = number of entering the
age.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">We
know m<sub>x</sub> = </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; top: 12pt;"><v:shape id="_x0000_i1025" style="height: 28.5pt; width: 12pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_CCA39032-DD88-4E3C-AB2C-AFB10AB48D53.0\msohtmlclip1\01\clip_image002.png">
</v:imagedata></v:shape></span><span style="font-size: 12pt; line-height: 115%;"> and q<sub>x</sub> =</span><span style="font-size: 14pt; line-height: 115%;"> </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; top: 12pt;"><v:shape id="_x0000_i1025" style="height: 28.5pt; width: 12pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_CCA39032-DD88-4E3C-AB2C-AFB10AB48D53.0\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><span style="font-size: 14pt; line-height: 115%;"> </span><span style="font-size: 12pt; line-height: 115%;">as per standard definition.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">Hence,<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;"> q<sub>x </sub></span><span style="font-size: 14pt; line-height: 115%;">= </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; top: 16pt;"><v:shape id="_x0000_i1025" style="height: 32.25pt; width: 45pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_CCA39032-DD88-4E3C-AB2C-AFB10AB48D53.0\msohtmlclip1\01\clip_image004.png">
</v:imagedata></v:shape></span><span style="font-size: 14pt; line-height: 115%;"> = </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; top: 18pt;"><v:shape id="_x0000_i1025" style="height: 35.25pt; width: 44.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_CCA39032-DD88-4E3C-AB2C-AFB10AB48D53.0\msohtmlclip1\01\clip_image005.png">
</v:imagedata></v:shape></span><span style="font-size: 14pt; line-height: 115%;"> = </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; position: relative; top: 12pt;"><v:shape id="_x0000_i1025" style="height: 28.5pt; width: 27.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_CCA39032-DD88-4E3C-AB2C-AFB10AB48D53.0\msohtmlclip1\01\clip_image006.png">
</v:imagedata></v:shape></span><span style="font-size: 14pt; line-height: 115%;"> </span><sub><span style="font-size: 14pt; line-height: 115%;"><o:p></o:p></span></sub></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 14pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN#3:<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">Column 3 is a probability of dying q<sub>x</sub>, is calculated as ASDR
or m<sub>x</sub>. ASDR is calculated as the ratio of no deaths to mid-year population,
where as q<sub>x </sub>is to be calculated as the ratio of no of deaths to the
no persons and tends to the age group.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">The assumption which we keep in consideration for construction of life
table is that the population is assumed to be closed. Hence; <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">NOTE: The last value of q<sub>x </sub>column must be less than or equal
to 1, because probability can not be greater than 1 in any circumstances.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN#4:<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">The number of survival is designated
as l<sub>x</sub> and started with a fixed known value at the first age l<sub>0</sub>
is equals to 100,000 as radix of the life table. We can take any round number
as a starting value. However commonly we take 100,000 as the radix of the life
table.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN#5:<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;">The number of deaths are then
estimated out of l<sub>x</sub> on the basis of probability of dying for an age
for example d<sub>0</sub>=l<sub>0</sub>*q<sub>0</sub>. As then the number of
survival for second age l<sub>1</sub> is determine by subtracting d<sub>0</sub>
from l<sub>0</sub>. Similarly d<sub>1</sub>=l<sub>1</sub>*q<sub>1</sub> and l<sub>2</sub>=
l<sub>1</sub>-d<sub>1</sub>and so on. In these calculations all values to be
taken as whole numbers, because they are number of death or survival (discrete
value).<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 12pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN#6:</span></i></b></div>
<div class="MsoListParagraphCxSpLast">
<span style="text-align: justify; text-indent: 1in;">Column
6 gives the number of years lived by all individuals between the age x </span><span style="text-align: justify; text-indent: 1in;"> </span><span style="text-align: justify; text-indent: 1in;">to x+1( x to x+1) and designated by l</span><sub style="text-align: justify; text-indent: 1in;">x</sub><span style="text-align: justify; text-indent: 1in;">.
Keeping the assumption of evenly distribution of number of deaths we get “L</span><sub style="text-align: justify; text-indent: 1in;">X</sub><span style="text-align: justify; text-indent: 1in;">=1/2
[lx+lx+1]”. For the last age group an approximation for L</span><sub style="text-align: justify; text-indent: 1in;">X</sub><span style="text-align: justify; text-indent: 1in;"> is given
by:</span></div>
<div class="MsoNormal" style="margin-left: .5in; text-align: justify; text-indent: 1.0in;">
<o:p></o:p></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14pt; line-height: 115%;">L<sub>99</sub> = l<sub>99</sub> * log<sub>10</sub>
l<sub>99</sub><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 14pt; line-height: 115%;"><sub><br /></sub></span></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN # 7:</span></i></b></div>
<div class="MsoNormal">
Column 7 gives number of years lived by all
individuals beyond age x and designated by T<sub>x</sub>. it is actually a
cumulative value of L<sub>x</sub> values from bottom of the live table.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-left: .5in;">
<o:p></o:p></div>
<div class="MsoNormal">
<b><i><span style="font-size: 12pt; line-height: 115%;">COLUMN # 8:<o:p></o:p></span></i></b></div>
<span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">Finally
expectation of live e<sup>0</sup><sub>x</sub> is obtained by dividing T<sub>x</sub>
coulumn#7 by the number of survivals l<sub>x</sub> given in column 4. This
figure indicates on an average the number of years to be lived by an individual
beyond his present age. First value of e<sup>0</sup><sub>x</sub> indicates the
overall or an average of an individual of the population for which the life
table has been constructed.</span><br />
<div class="MsoListParagraphCxSpLast">
<span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;"><br /></span></div>
</div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-6449584934586077862012-04-13T12:50:00.002-07:002012-04-13T12:50:41.120-07:00ERROR IN AGE REPORTING AND THEIR METHODS<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">In
demographic data the most important and common error is committed in recording
of ages. Ages are recorded in whole numbers in completed years. Extract date of
birth are seldom asked, even if exact date of birth are known, the date is
tabulated with a reference to date in incomplete year which creates biased over
above ages are misstated due to conscious acts and same times unconsciously
wrong ages are recorded. Studies of various ages data revealed that following
type of misstatement of ages are usually recorded.</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span><br />
<a name='more'></a><br /><br />
<br />
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; line-height: 115%;">Over Statement of Ages of Children/
Infants:<o:p></o:p></span></b></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> An over statement of ages before adult hood and under statement
afterward. An over statement of ages of person just below 65 years an over
statement of ages toward extreme of life. A heaping of ages at 21 years for
male and 18 years for female. Heaping of ages of ending digits which are
multiple of 5 that are 0 and 5 there after even digits or odd digits ages not
studies not recorded not stated or unknown.</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span><br />
<br />
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; line-height: 115%;">Methods of Studying Error in Age
Reporting:<o:p></o:p></span></b></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Various method of studying and measuring error in ages reporting have
been develop some of them are objectives and other are subjective. First among
them is to see presence of digits preference by contracting what we call the POPULATION
PYRAMID taking population on axis such
that one side male and on the other side female population is taken with ages
on y-axis. Ages may be taken in single year or 5 years interval. From
theoretical assumption if the population is closed to migration pyramid should
smooth triangle, however this is not the case as the mortality pattern every
age is not same and also the sex differential. The pyramid also reveals level
and pattern of fertility and mortality.</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span><br />
<br />
<div class="MsoNormal">
Subjective method of detecting miss-reporting of ages is
based on comparisons of data. Comparison is possible with in and between the
data of two series. Another comparison is possible with the last census or the
survey result. A group of persons who are in age group 5 to 90 in a particular
census will be 15 to 90 years of age after 10 years that is at second census
with possible reduction due to mortality keeping population close to migration.
A closed data examination reveals that there are consternation of persons at
ages, ending at (0 and 5) and even digits. This is attributed to wrong
recording of ages. Because this is not possible that births occur at such
interval as to have lesser number of person of ages ending at odd digits at a
particular time.<o:p></o:p></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The indexes which are use in measuring it are:</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">1. </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">Whipple’s
Index.</span><br />
<span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">2. </span><span style="text-indent: -0.25in;">UN Secretariat Method.</span><br />
<span style="text-indent: -0.25in;">3. </span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%;">Myer’s
Index.</span><br />
<span style="text-indent: -0.25in;"><br /></span><br />
<br />
<div class="MsoListParagraphCxSpFirst">
<b><span style="font-size: 14.0pt; line-height: 115%;">WHIPPLE’S INDEX:</span></b></div>
<div class="MsoListParagraphCxSpFirst">
Whipple’s Index
reflects the age heaping on multiple five that is terminal digit (0 and 5) with
in the age range from 23 to 62 years hence Whipple’s Index is defined as</div>
<div class="MsoListParagraphCxSpMiddle">
<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4bG3K26_QfOjKoiTKqlu_hs7GB_A_JvIaOEpSm3mkbPuTgNXWwhogVe1T2sDm-Gof_cuSYotMUgaxlkkgJwFNeDq66puuLwxjo6DFHzfhWzFcqRzyKMec4wd9NfFAJkZLRVXlrAXuoZ2j/s1600/Capture+1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4bG3K26_QfOjKoiTKqlu_hs7GB_A_JvIaOEpSm3mkbPuTgNXWwhogVe1T2sDm-Gof_cuSYotMUgaxlkkgJwFNeDq66puuLwxjo6DFHzfhWzFcqRzyKMec4wd9NfFAJkZLRVXlrAXuoZ2j/s1600/Capture+1.PNG" /></a></div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
<span style="font-size: 16.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
Approximate 100 values of Whipple’s Index are
for low preference. Well it exceed 175 the quality of age data is very rough as
for UN standard. Maximum value of WI is 500 indicating that only zero and five
(0-5) ending digit has been recorded.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraphCxSpFirst">
<b><span style="font-size: 14.0pt; line-height: 115%;">UN SECRETARIAT METHOD:<o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpLast">
The method is
applied when we have data in 5 years age interval. In this method sex ratio and
age ratio for 5 years age group are found up to 70 years. In case of sex ratio
successively differences between one age group and the next age are found and
their average is taken without considering algebraic signs.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2CDfhmgAzavXPq7hlFTso7S5DqEB3ONbPtbkLpReHCpN19G6xe21SOttFn6ULIyrA3P-P_EO3xbkfd6-tl14CL0Ei6SI_9DPdSiRMs2AtW2spOKpiiU7wvhn3lCTiO58u-v78akuYfnu-/s1600/Capture+2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2CDfhmgAzavXPq7hlFTso7S5DqEB3ONbPtbkLpReHCpN19G6xe21SOttFn6ULIyrA3P-P_EO3xbkfd6-tl14CL0Ei6SI_9DPdSiRMs2AtW2spOKpiiU7wvhn3lCTiO58u-v78akuYfnu-/s1600/Capture+2.PNG" /></a></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpFirst">
In case of age ratio for sex deviation from
100 are obtained and averaged of unrespectable of algebraic sign.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-size: 14.0pt; line-height: 115%;">U.N.S. = 3 {Mean of |SR|} + Mean of |Average Ratio Male| + Mean of
|Average ratio of female|<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Three times the average of sex ratio differences
is then add to the two averages of the deviation of the age ratio from 100 to
complete the index. The resulting index is not exact and should by regarded as
order of magnitude rather than a precise measurement.</span><br />
<div class="MsoListParagraphCxSpLast">
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraph">
<b><span style="font-size: 14.0pt; line-height: 115%;">MYER’S INDEX:<o:p></o:p></span></b></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">A method of blended
population suggested by MYER for obtaining the number of persons at ages ending
with digits 0 to 9 starting from 10 years onwards and then starting from 20
years onwards. The population at each digit in first case is given the weights
as 1, 2, 3 … 10 and population in second case is given the weights as 9, 9, 7…
0. Then the weighted average of these two populations has found and termed as
blended population.</span><br />
<div class="MsoListParagraphCxSpLast">
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP-QXWoCFLfS7AqcoX5nHuLFx5-Wcr69UGOdfEHMGOLcSXLJFUFojA7CtqBWpD354sVvX0974V940xMTfvGKIta5b9nj4nxsAxmTHLtiiSnypRAh9zq9uGYwal61D6dB8zu1LmwCCDhtGp/s1600/Capture+3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP-QXWoCFLfS7AqcoX5nHuLFx5-Wcr69UGOdfEHMGOLcSXLJFUFojA7CtqBWpD354sVvX0974V940xMTfvGKIta5b9nj4nxsAxmTHLtiiSnypRAh9zq9uGYwal61D6dB8zu1LmwCCDhtGp/s1600/Capture+3.PNG" /></a></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoNormal">
The range for the two populations must be kept same. The
data below age 10 and after age 80 is usually not consider for forming Blended
population (BP) as the accuracy of information is highly questionable.<o:p></o:p></div>
<div class="MsoNormal">
The blended population of digit 9 is made the unit of
comparison and the ratio is found. A ratio of 1 shows low preference for the
digit and the ratio of more than 1 show more preference.<o:p></o:p></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Another way of finding the digital preference is
to measure accuracy of the total BP of each digit. A extend of preference is
indicated by the preference deviation from 10%. In order to measure the total
amount of error in age reporting for a population Myer drive the preference
which is simply a sum of absolute deviation from 10%. In the absence of error
its index is zero and maximum value is 180.</span><br />
<div class="MsoListParagraphCxSpLast">
<span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: EN-US; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoNormal">
MYERS INDEX DEVIATION POPULATION (MIDP)<o:p></o:p></div>
<div align="center" class="MsoNormal" style="text-align: center;">
MIDP= ∑ |column (10 –
11)|<o:p></o:p></div>
<br />
<br />
<br />
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<o:p></o:p></div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-90368039445852051292012-04-13T12:02:00.001-07:002012-04-19T17:46:04.160-07:00MEASUREMENT OF ERRORS IN DEMOGRAPHIC DATA<div dir="ltr" style="text-align: left;" trbidi="on">
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mso-bidi-theme-font:major-bidi;
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h2
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h3
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h4
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margin-bottom:.0001pt;
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h5
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h6
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p.MsoTitle, li.MsoTitle, div.MsoTitle
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margin-bottom:10.0pt;
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margin-right:0in;
margin-bottom:10.0pt;
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p.MsoSubtitle, li.MsoSubtitle, div.MsoSubtitle
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margin-right:0in;
margin-bottom:30.0pt;
margin-left:0in;
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em
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p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
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span.MsoPlaceholderText
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p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
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p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
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p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
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p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
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margin-right:.25in;
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p.MsoIntenseQuote, li.MsoIntenseQuote, div.MsoIntenseQuote
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margin-bottom:14.0pt;
margin-left:.7in;
text-align:justify;
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span.MsoSubtleEmphasis
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mso-style-parent:"";
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span.MsoIntenseEmphasis
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span.MsoSubtleReference
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span.MsoIntenseReference
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text-underline:single;}
span.MsoBookTitle
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p.MsoTocHeadingCxSpFirst, li.MsoTocHeadingCxSpFirst, div.MsoTocHeadingCxSpFirst
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<div class="MsoNormal">
Methods of measurements of errors have been developed for
census statistics; however can equally be used in vital statistics
registration.</div>
<div class="MsoNormal">
Response error is a broad term which includes both errors of
coverage and error of content. The sampling theory assumed the census or survey
or VSR records collected at time period are regarded as one of the series of trials,
collection of responses which would vary from trial to trial. This hypothesis
further assumed that the trials have been conducted under the same conditions
and that they are independent of each other.</div>
<div class="MsoNormal">
Various indices, measuring levels of errors can be
calculated through this table:<br />
<br />
<a name='more'></a><br /></div>
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<tbody>
<tr style="height: 15.75pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td colspan="5" style="border: solid windowtext 1.0pt; height: 15.75pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 441.2pt;" valign="top" width="588"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Count in Census(Ideal/ Standard) / Survey<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 37.75pt; mso-yfti-irow: 1;">
<td rowspan="4" style="border-bottom: solid windowtext 1.0pt; border-left: solid windowtext 1.0pt; border-right: solid black 1.0pt; border-top: none; height: 37.75pt; mso-border-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 55.35pt;" valign="top" width="74"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">C<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">O<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">N<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">T<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">E<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">N<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">E<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">V<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">A<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">L<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">U<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">T<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">I<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">O<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b style="mso-bidi-font-weight: normal;">Survey<o:p></o:p></b></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<br /></div>
</td>
<td colspan="2" style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 37.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 196.75pt;" valign="top" width="262"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
Number of persons in count</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 37.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 129.4pt;" valign="top" width="173"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
Number of Person not in count</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 37.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 59.7pt;" valign="top" width="80"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
Total</div>
</td>
</tr>
<tr style="height: 105.25pt; mso-yfti-irow: 2;">
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 105.25pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-alt: solid windowtext .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 52.75pt;" valign="top" width="70"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
Number of person in class</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 105.25pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
a</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 105.25pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 129.4pt;" valign="top" width="173"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
b</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 105.25pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 59.7pt;" valign="top" width="80"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
a+b</div>
</td>
</tr>
<tr style="height: 73.75pt; mso-yfti-irow: 3;">
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 73.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-alt: solid windowtext .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 52.75pt;" valign="top" width="70"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
Number of person not in class</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 73.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
C</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 73.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 129.4pt;" valign="top" width="173"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
d</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 73.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 59.7pt;" valign="top" width="80"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
c+d</div>
</td>
</tr>
<tr style="mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-alt: solid windowtext .5pt; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 52.75pt;" valign="top" width="70"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
Total </div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 2.0in;" valign="top" width="192"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
a+c</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 129.4pt;" valign="top" width="173"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
b+d</div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 59.7pt;" valign="top" width="80"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<br /></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l4 level1 lfo5; text-indent: -.25in;">
<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span>Then (a+c) represent count in a census/ sample
survey/ VSR in relation to birth, death etc.</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l4 level1 lfo5; text-indent: -.25in;">
<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span>(a+b) is the corresponding count in CES </div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l4 level1 lfo5; text-indent: -.25in;">
<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span> “a”
is the number appearing in both</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l4 level1 lfo5; text-indent: -.25in;">
<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span>And on the other hand c would occur in actual</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l4 level1 lfo5; text-indent: -.25in;">
<span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span></span>And “d” is the number without count
characteristic and vital counts.</div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 40.5pt; mso-add-space: auto; mso-list: l1 level1 lfo1; mso-text-indent-alt: -.25in; text-indent: -40.5pt;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>i.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>Net difference rate (NDR).</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 40.5pt; mso-add-space: auto; mso-list: l1 level1 lfo1; mso-text-indent-alt: -.25in; text-indent: -40.5pt;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>ii.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>Gross difference rate (GDR).</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 40.5pt; mso-add-space: auto; mso-list: l1 level1 lfo1; mso-text-indent-alt: -.25in; text-indent: -40.5pt;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>iii.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>The index of net shift relative to ideal or
standard count.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 40.5pt; mso-add-space: auto; mso-list: l1 level1 lfo1; mso-text-indent-alt: -.25in; text-indent: -40.5pt;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>iv.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>Index of stability.</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 40.5pt; mso-add-space: auto; mso-list: l1 level1 lfo1; mso-text-indent-alt: -.25in; text-indent: -40.5pt;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>v.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>Index of inconsistency.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l3 level1 lfo2; text-indent: -.25in;">
<span style="font-size: 14pt; line-height: 115%;">1)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span style="font-size: 14pt; line-height: 115%;">NET DIFFERENCE RATE (NDR):<o:p></o:p></span></u></div>
<div class="MsoListParagraphCxSpMiddle">
The net difference rate is defined as</div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
<span style="font-size: 19px; line-height: 21px;">NDR=(c-b)/n *100</span></div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
<span style="font-size: 19px; line-height: 21px;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
It provides an estimate of the extent of
the biased in the actually observed count (a+c). A positive value of the rate
indicates an over statement, while a negative value indicates an under count in
census survey or VSR. In case of no error the value would be zero.</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l3 level1 lfo2; text-indent: -.25in;">
<span style="font-size: 14pt; line-height: 115%;">2)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span style="font-size: 14pt; line-height: 115%;">GROSS DIFFERENCE RATE:<o:p></o:p></span></u></div>
<div class="MsoListParagraphCxSpMiddle">
GDR assumed in a hypothetical situation of repeated response from the
same person in a large series of census/survey or VSR conducted under same
conditions that a record is made of the response deviation for some person on
each trial from the average of all responses. Hence the gross difference rate
is defined as </div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
</div>
<div align="center" class="MsoListParagraph">
<span style="font-size: 14pt; line-height: 115%;">g= </span><span style="font-size: 14pt; line-height: 115%;">b+c/n*100<o:p></o:p></span></div>
<br />
<div class="MsoListParagraphCxSpMiddle">
And the simple response variance is
approximated as;<o:p></o:p></div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
<span style="font-size: 14pt; line-height: 115%;">SRV =</span><span style="font-size: 14pt; line-height: 115%;">1/2g<o:p></o:p></span><br />
<span style="font-size: 14pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l3 level1 lfo2; text-indent: -.25in;">
<span style="font-size: 14pt; line-height: 115%;">3)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span style="font-size: 14pt; line-height: 115%;">The index of net shift relative to
ideal standard count:<o:p></o:p></span></u></div>
<div class="MsoListParagraphCxSpMiddle">
It is defined as the ratio of the differences in the count with the
total in ideal count. Its positive indicates over estimate and negative
indicates an under count.</div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
<span style="font-size: 14pt; line-height: 115%;">s =</span><span style="font-size: 14pt; line-height: 115%;">c-b/a+b*100<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l3 level1 lfo2; text-indent: -.25in;">
<span style="font-size: 14pt; line-height: 115%;">4)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span style="font-size: 14pt; line-height: 115%;">Index of stability:<o:p></o:p></span></u></div>
<div class="MsoListParagraphCxSpMiddle">
The index of stability is a ratio which shows a number with specified
characteristics which included in both, the census/ survey/ VSR with relation
to those characteristics in the ideal or standard count. In terms of notation
adopted this index is defined as:</div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
<span style="font-size: 14pt; line-height: 115%;">Index of stability= </span><span style="font-size: 14pt; line-height: 115%;">a/a+b*100<o:p></o:p></span><br />
<span style="font-size: 14pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpLast">
This indicates the stability of response,
the census survey or VSR relative to the ideal or standard count.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l3 level1 lfo2; text-indent: -.25in;">
<span style="font-size: 14pt; line-height: 115%;">5)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span style="font-size: 14pt; line-height: 115%;">Index of consistency:<o:p></o:p></span></u></div>
<div class="MsoListParagraphCxSpMiddle">
The index of consistency which is also the measure of the stability of
response is defined as;<o:p></o:p></div>
<div align="center" class="MsoListParagraphCxSpMiddle" style="text-align: center;">
<span style="font-size: 14pt; line-height: 115%;">I = </span><span style="font-size: 14pt; line-height: 115%;">g/2p(1-p)*100</span><br />
<span style="font-size: 14pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
Where p (1-p) is estimated by the average
of sampling variance of the proportion having same characteristics such as
specified occupation in census survey or VSR in the ideal situation or standard
count.</div>
<div class="MsoListParagraphCxSpMiddle">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;">Census/ Survey/ VSR<o:p></o:p></span></b><br />
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;"><br /></span></b><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgNDZeGQKLRP2Uwh54jTlvowBvfVxVTreNHTkj8oj2_uyY2SAtbs5tpS5yN4KnszEBv6guNgiCYOxOsjJ2Eyr_s8E_dDfQpUHTZKZRyWIu1xLrAQ43WR6Pr5GEjOpY8gis5XlY3Be8EuW5/s1600/error+pic.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgNDZeGQKLRP2Uwh54jTlvowBvfVxVTreNHTkj8oj2_uyY2SAtbs5tpS5yN4KnszEBv6guNgiCYOxOsjJ2Eyr_s8E_dDfQpUHTZKZRyWIu1xLrAQ43WR6Pr5GEjOpY8gis5XlY3Be8EuW5/s400/error+pic.PNG" width="400" /></a></div>
<div style="text-align: center;">
</div>
<div class="MsoListParagraphCxSpFirst" style="text-align: left;">
<span style="font-size: small;"><span style="line-height: 18px;"><b><br /></b></span></span></div>
</div>
<div class="MsoNormal" style="tab-stops: 150.75pt;">
<br />
Generally I vary between
0 ≤ I ≤100
<o:p></o:p></div>
<div class="MsoListParagraphCxSpFirst" style="tab-stops: 150.75pt;">
However
values of I greater than 100 may arise occasionally when small sample are
involved or if the assumption of estimation is completely not valid. A large
value of I indicates a high degree of response error, an index of the stability
of response “r” is more readily understood than I.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="tab-stops: 150.75pt;">
However
it should be recognized that I and r are complementary in the sense that a
large number of response error by a large value of I and by a small value of
“r”.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="tab-stops: 150.75pt;">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="tab-stops: 150.75pt;">
<br /></div>
</div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-91157105563145172982012-03-29T07:56:00.001-07:002012-04-19T17:46:04.163-07:00ERRORS IN DEMOGRAPHIC DATA<div dir="ltr" style="text-align: left;" trbidi="on">
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mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
mso-style-unhide:no;
mso-style-qformat:yes;
margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:.5in;
mso-add-space:auto;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;}
p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
{mso-style-priority:34;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-type:export-only;
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
margin-bottom:.0001pt;
mso-add-space:auto;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;}
p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
{mso-style-priority:34;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-type:export-only;
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
margin-bottom:.0001pt;
mso-add-space:auto;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;}
p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
{mso-style-priority:34;
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mso-style-qformat:yes;
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margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:.5in;
mso-add-space:auto;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;}
p.MsoQuote, li.MsoQuote, div.MsoQuote
{mso-style-priority:29;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-link:"Quote Char";
mso-style-next:Normal;
margin-top:10.0pt;
margin-right:.25in;
margin-bottom:0in;
margin-left:.25in;
margin-bottom:.0001pt;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;
font-style:italic;}
p.MsoIntenseQuote, li.MsoIntenseQuote, div.MsoIntenseQuote
{mso-style-priority:30;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-link:"Intense Quote Char";
mso-style-next:Normal;
margin-top:10.0pt;
margin-right:.8in;
margin-bottom:14.0pt;
margin-left:.7in;
text-align:justify;
line-height:115%;
mso-pagination:widow-orphan;
border:none;
mso-border-bottom-alt:solid windowtext .5pt;
padding:0in;
mso-padding-alt:0in 0in 1.0pt 0in;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;
font-weight:bold;
font-style:italic;}
span.MsoSubtleEmphasis
{mso-style-priority:19;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
font-style:italic;}
span.MsoIntenseEmphasis
{mso-style-priority:21;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
font-weight:bold;}
span.MsoSubtleReference
{mso-style-priority:31;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
font-variant:small-caps;}
span.MsoIntenseReference
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mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
font-variant:small-caps;
letter-spacing:.25pt;
text-decoration:underline;
text-underline:single;}
span.MsoBookTitle
{mso-style-priority:33;
mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
font-variant:small-caps;
letter-spacing:.25pt;
font-style:italic;}
p.MsoTocHeading, li.MsoTocHeading, div.MsoTocHeading
{mso-style-noshow:yes;
mso-style-priority:39;
mso-style-qformat:yes;
mso-style-parent:"Heading 1";
mso-style-next:Normal;
margin-top:24.0pt;
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margin-bottom:0in;
margin-left:0in;
margin-bottom:.0001pt;
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font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
mso-ascii-theme-font:major-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:major-fareast;
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mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
mso-bidi-language:EN-US;
font-weight:bold;}
p.MsoTocHeadingCxSpFirst, li.MsoTocHeadingCxSpFirst, div.MsoTocHeadingCxSpFirst
{mso-style-noshow:yes;
mso-style-priority:39;
mso-style-qformat:yes;
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mso-style-type:export-only;
margin-top:24.0pt;
margin-right:0in;
margin-bottom:0in;
margin-left:0in;
margin-bottom:.0001pt;
mso-add-space:auto;
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font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:major-fareast;
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mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
mso-bidi-language:EN-US;
font-weight:bold;}
p.MsoTocHeadingCxSpMiddle, li.MsoTocHeadingCxSpMiddle, div.MsoTocHeadingCxSpMiddle
{mso-style-noshow:yes;
mso-style-priority:39;
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mso-style-type:export-only;
margin:0in;
margin-bottom:.0001pt;
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line-height:115%;
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
mso-bidi-language:EN-US;
font-weight:bold;}
p.MsoTocHeadingCxSpLast, li.MsoTocHeadingCxSpLast, div.MsoTocHeadingCxSpLast
{mso-style-noshow:yes;
mso-style-priority:39;
mso-style-qformat:yes;
mso-style-parent:"Heading 1";
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mso-style-type:export-only;
margin:0in;
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mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
mso-bidi-language:EN-US;
font-weight:bold;}
span.Heading1Char
{mso-style-name:"Heading 1 Char";
mso-style-priority:9;
mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:"Heading 1";
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
font-weight:bold;}
span.Heading2Char
{mso-style-name:"Heading 2 Char";
mso-style-noshow:yes;
mso-style-priority:9;
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mso-style-link:"Heading 2";
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font-family:"Cambria","serif";
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mso-ascii-theme-font:major-latin;
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
font-weight:bold;}
span.Heading3Char
{mso-style-name:"Heading 3 Char";
mso-style-priority:9;
mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:"Heading 3";
font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
font-weight:bold;}
span.Heading4Char
{mso-style-name:"Heading 4 Char";
mso-style-noshow:yes;
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mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:"Heading 4";
font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-fareast-theme-font:major-fareast;
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mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
font-weight:bold;
font-style:italic;}
span.Heading5Char
{mso-style-name:"Heading 5 Char";
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mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:"Heading 5";
font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
color:#7F7F7F;
mso-themecolor:text1;
mso-themetint:128;
font-weight:bold;}
span.Heading6Char
{mso-style-name:"Heading 6 Char";
mso-style-noshow:yes;
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mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:"Heading 6";
font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
color:#7F7F7F;
mso-themecolor:text1;
mso-themetint:128;
font-weight:bold;
font-style:italic;}
span.Heading7Char
{mso-style-name:"Heading 7 Char";
mso-style-noshow:yes;
mso-style-priority:9;
mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:"Heading 7";
font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
font-style:italic;}
span.Heading8Char
{mso-style-name:"Heading 8 Char";
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mso-style-link:"Heading 8";
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font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
mso-ascii-theme-font:major-latin;
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;}
span.Heading9Char
{mso-style-name:"Heading 9 Char";
mso-style-noshow:yes;
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mso-style-link:"Heading 9";
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font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
letter-spacing:.25pt;
font-style:italic;}
span.TitleChar
{mso-style-name:"Title Char";
mso-style-priority:10;
mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:Title;
mso-ansi-font-size:26.0pt;
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font-family:"Cambria","serif";
mso-ascii-font-family:Cambria;
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
letter-spacing:.25pt;}
span.SubtitleChar
{mso-style-name:"Subtitle Char";
mso-style-priority:11;
mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:Subtitle;
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font-family:"Cambria","serif";
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mso-fareast-theme-font:major-fareast;
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mso-hansi-theme-font:major-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:major-bidi;
letter-spacing:.65pt;
font-style:italic;}
span.QuoteChar
{mso-style-name:"Quote Char";
mso-style-priority:29;
mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:Quote;
font-style:italic;}
span.IntenseQuoteChar
{mso-style-name:"Intense Quote Char";
mso-style-priority:30;
mso-style-unhide:no;
mso-style-locked:yes;
mso-style-link:"Intense Quote";
font-weight:bold;
font-style:italic;}
span.GramE
{mso-style-name:"";
mso-gram-e:yes;}
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{mso-style-type:export-only;
mso-default-props:yes;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Calibri;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;
mso-bidi-language:EN-US;}
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{mso-style-type:export-only;
margin-bottom:10.0pt;
line-height:115%;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
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mso-list-type:hybrid;
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text-indent:-.25in;}
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text-indent:-9.0pt;}
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text-indent:-9.0pt;}
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text-indent:-.25in;}
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text-indent:-.25in;}
@list l0:level9
{mso-level-number-format:roman-lower;
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text-indent:-9.0pt;}
@list l1
{mso-list-id:551162207;
mso-list-type:hybrid;
mso-list-template-ids:1764811360 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
@list l1:level1
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text-indent:-.25in;}
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{mso-level-number-format:alpha-lower;
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text-indent:-.25in;}
@list l1:level3
{mso-level-number-format:roman-lower;
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mso-level-number-position:right;
text-indent:-9.0pt;}
@list l1:level4
{mso-level-tab-stop:none;
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<br />
<div class="WordSection1">
<div class="MsoNormal">
Despite the care
taken to ensure the quality of the data collected by enumeration and
registration, it will some time give obvious indications of errors in basic
information. Usually errors in censuses and vital statistic registration (VSR)
are of two types:<br />
<a name='more'></a></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l4 level1 lfo1; text-indent: -.25in;">
1.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>Coverage.</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l4 level1 lfo1; text-indent: -.25in;">
2.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>Content.</div>
<div class="MsoListParagraphCxSpLast">
A third type of error is
sampling error which is introduced when sampling is used.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo3; text-indent: -.25in;">
<span style="font-size: 16pt; line-height: 115%;">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span style="font-size: 16pt; line-height: 115%;">ERROR OF COVERAGE:<o:p></o:p></span></u></div>
<div class="MsoListParagraphCxSpLast">
It is the common observation that a conduct or survey some households
are missed and not counted, others may be counted two times. In VSR (vital
statistic registration) there are cases which skip in registration (birth,
date, marriages) these situation errors in demographic data offer must be made
to cover all units and events of all observations which fall in our domain.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo3; text-indent: -.25in;">
<span style="font-size: 16pt; line-height: 115%;">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span><u><span style="font-size: 16pt; line-height: 115%;">ERRORS IN CONTENT:<o:p></o:p></span></u></div>
<div class="MsoListParagraphCxSpMiddle">
The term error of content refers to instance where the characteristic of
a person counted in a census enumeration or in registration or in a survey are
in correctly reported, recorded and tabulated or sometime they are completely
missing.</div>
<div class="MsoListParagraphCxSpMiddle">
Besides from the errors due to carelessness or mistakes in judgment in a
census or VSR, errors of coverage or content or both can arise at any step from
initiation of an original record publication to the final tabulation or final
record. The five principles are:</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo4; mso-text-indent-alt: -.25in; text-indent: -1.0in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>i.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>The respondent.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo4; mso-text-indent-alt: -.25in; text-indent: -1.0in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>ii.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>The recorder/ enumerator /investigator.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo4; mso-text-indent-alt: -.25in; text-indent: -1.0in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>iii.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>The coding process.</div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo4; mso-text-indent-alt: -.25in; text-indent: -1.0in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>iv.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>The editing process.</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo4; mso-text-indent-alt: -.25in; text-indent: -1.0in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>v.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>Compiling and printing process.</div>
<div class="MsoNormal">
The
respondent error may be occur due to ignorance, illiteracy or will full wrong
answer. For example: a person may not remember his/her correct age or he/she
may will fully give wrong age or income etc. sometimes the respondent does not
understand the question and give wrong information, this type of errors known
as respondent error. </div>
<div class="MsoNormal">
The second source of error is one part of enumerator who may not listen
correctly or may made wrong entries. The errors at the stage of coding, editing
and classification are quiet common. Placing of code at the right place is very
much necessary. Editors have to give extra care in comparing logical answer of
similar and related question. Similarly at the time of classification,
tabulation and printing certain error do crept.</div>
<div class="MsoNormal">
<u><span style="font-size: 16pt; line-height: 115%;">DETECTION
OF ERRORS:<o:p></o:p></span></u></div>
<div class="MsoNormal">
In VSR errors may be detected by comparison of either tabulated data or
individual records. Comparisons of tabulated data may yield or may be made
either by internal comparison with previous census results or comparison with
independent collateral data. Internal comparison may <span class="GramE">revealed</span>
inconsistency between related data in the tabulated result ratio to male or
female for ages at some stages of life may appear to be out of line. Comparison
can be made with previous census and vital statistics. For example: a census
may shoe fewer or more persons in an age group than expected keeping in mind
mortality and migration patterns.</div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l2 level1 lfo5; mso-text-indent-alt: -.25in; text-indent: -.5in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>i.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>COMPARISON WITH COLLATERAL DATA means to look at
related independent data that is number of children in schools, number of
buses, housing unit, electric meters etc.</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo5; mso-text-indent-alt: -.25in; text-indent: -.5in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>ii.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>COMPARISON OF INDIVIDUAL RECORDS census return
of individual is critically examined with reference to itself and some other
co-lateral records’. Registration of individual tax return etc.</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo5; mso-text-indent-alt: -.25in; text-indent: -.5in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>iii.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span> RE-ENUMERATION SURVEY/ POST ENUMERATION
SURVEY</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo5; mso-text-indent-alt: -.25in; text-indent: -.5in;">
<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span>iv.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;">
</span>In order to check the quality of census returns
a re-enumeration survey or post enumeration survey is conducted on selected
units. This survey is conducted by senior professionals and all efforts are
being made to obtain accurate records. Schedules of these surveys are than
compared with census returns. To measure the error of content, the post
enumeration survey is sometimes known as content evaluation survey (CES) and it
is supposed to be accurate among all exercise.</div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div class="MsoNormal">
<br /></div>
</div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-4372140744132319612012-03-26T08:17:00.002-07:002012-03-26T10:06:37.255-07:00CENSUS<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">The literally meaning of the census to count every
individual unit in a well defines territory at a moment of time and records
some vital event of every individual. According to U.N. “<i>census of human population is defined as the total process of
collecting, compiling and publishing demographic, economic and social data
pertaining to all person at a specified time or times in a country or
de-limited territory”</i>. U.N. has listed four essential features of
population censuses.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"></span><br />
<a name='more'></a><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
</div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">1.<span style="font-size: 7pt;">
</span>Each individual is too enumerated separately and
the characteristics of each person are recorded separated.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">2.<span style="font-size: 7pt;">
</span>The census covers precisely defined territory
and includes every person present and reseeding with in its scope.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">3.<span style="font-size: 7pt;">
</span>The population is enumerated with respect to a
well defined point of time and data are prepared in terms of well defined
references period.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">4.<span style="font-size: 7pt;">
</span>The census must be taking at regular interval.</span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">A census is prim alary an official enumeration through
direct visitation of all persons either physically present or regular reciting
in a country or any of its division. The enumeration includes the collection of
various data concerning the person enumerated, such as sex, age, marital status
etc. however, there may be special census for specific purposes for example
occupation, employment, education etc.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .75in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><u></u></span><br />
<h1>
<u><span style="font-family: 'Trebuchet MS', sans-serif;">CHARACTERISTICS
OF AN IDEAL CENSUS</span></u></h1>
</div>
<div class="MsoNormal">
<u><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 14pt; line-height: 115%;"><br /></span></u></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">There are some characteristics of an ideal census which are
given as follows:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoNormal">
</div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">·<span style="font-size: 7pt;"> <b>
</b></span><b>UNIVERSAL -</b> An ideal census must be
universal in character it mean there should be information about every citizen
of a country.</span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">·<span style="font-size: 7pt;">
</span><b>POINT OF TIME -</b> All information
relating to population should be connected with reference to a particular point
of time otherwise different magnitude can not be compared.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">·<span style="font-size: 7pt;">
</span><b>AREA -</b> Census should be conducted in a well define state or country.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">·<span style="font-size: 7pt;">
</span><b>AFTER A DEFINITE PERIOD -</b> Census should be undertaken after a
definite interval or period of time. It is generally conducted after 10 years
and called “Decennial Census” and in some countries censuses is conducted after
5 years and known as “Quinquennial Census” by government.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">·<span style="font-size: 7pt;">
</span><b>UNDER LEGAL GOVERNMENT -</b> Census is always to be carried out by legal government and not by any
private agency under specific legal cover.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;">·<span style="font-size: 7pt;">
</span><b>SECRET AND CONFIDENCIAL -</b> In a census complete information
about individuals should be collected and must be kept secret and confidential.
All information of total population be complied together and totally be
disseminated through propagation and publication.</span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
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<span style="font-family: 'Trebuchet MS', sans-serif;">·<span style="font-size: 7pt;">
</span><b>UNIVERSE IS UNITED -</b> In a
census the entire universe is united their by possibility of any sampling error
and biased are not arrived. However presence of non sampling error can not be
ruled out. </span></div>
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</div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"> Some of the non sampling error which are present in
census.<o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">a.<span style="font-size: 7pt;">
</span>Coverage<o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">b.<span style="font-size: 7pt;">
</span>Content (response and record)<o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">c.<span style="font-size: 7pt;">
</span>Measurement (education, age)<o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">d.<span style="font-size: 7pt;">
</span>Compilation, processing and printing.<o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">In census as the data collected in mass therefore there is
every possibility of extremes being neutralized However, census data has to be
kept comparable and compactable in time places, quantities, units and formats.<o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><u></u></span><br />
<h1>
<u><span style="font-family: 'Trebuchet MS', sans-serif;">HISTORICAL
BACKGROUND</span></u></h1>
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<u><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 14pt; line-height: 115%;"><br /></span></u></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">History of census count data back to be great civilization of <b>Baby
Leonia in 3800 BC</b>, <b>china in 3000 BC</b> and <b>Egypt in 2500 BC</b> and Greek and Roman
period. However record of these counts is not press able, only few results
survive which indicates the counting of population was made in those
civilizations.<o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">Most of these
counts are population like the English the doomsday inquest of 1086 were
partial encourage because of rather limited use to which these data were put.
Generally they were limited to land holders and head of household or males of
military age or tax pears and work for military labor and tax purposes.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: 'Trebuchet MS', sans-serif;">Modern censuses
begin with the enumeration of population in <b>Quebec in 1666</b>. The periodic census
as a regular function of government dates from <b>1790 in USA</b>, 1801 in England and
1871 in Canada. During 1950-1953 census of population were conducted in 41
sovereign countries and also in a large number of non sovereign countries it
included about (3/5)th of the total population of the world. In 1963 about 192
countries of the world conducted census. Nowadays there are only 11 countries
(6 in Africa, 5 in Asia) with a population exceeding 5000 people have not
conducted census so far.<o:p></o:p></span></div>
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-205697870865241822012-03-24T09:30:00.002-07:002012-03-24T09:30:30.677-07:00TRADE - OFF THEORY<div dir="ltr" style="text-align: left;" trbidi="on">
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<div class="separator" style="clear: both; text-align: center;">
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<span style="font-family: 'Trebuchet MS', sans-serif;">“<b>THE TRADE-OFF THEORY OF LEVERAGE</b>”, in which firms’ trade
off the benefits of debt financing against the higher interest rates and
bankruptcy costs. A summary of the trade-off theory is expressed in figure. Here
are some observations about the figure:</span><br />
<a name='more'></a><o:p></o:p></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtXKuYXyFJdDiH0hD6C2nZF37CrculS93PZxA6dk4Xv2ADH7u-Wp1ycbJerj1cwvYFdQ1i1siJX2dNOfbYaoaIYW4ap6YnpvvO_JVQSyxjRboynJ7VpHdyxHz9tpuSFYZOgcdbwNE1CmtZ/s1600/Capture.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtXKuYXyFJdDiH0hD6C2nZF37CrculS93PZxA6dk4Xv2ADH7u-Wp1ycbJerj1cwvYFdQ1i1siJX2dNOfbYaoaIYW4ap6YnpvvO_JVQSyxjRboynJ7VpHdyxHz9tpuSFYZOgcdbwNE1CmtZ/s1600/Capture.PNG" title="Trade-off theory - actuarial science" /></a></td></tr>
<tr><td class="tr-caption">THE TRADE-OFF THEORY OF LEVERAGE <span style="font-family: 'Trebuchet MS', sans-serif; font-size: small;"><b><br /></b></span></td></tr>
</tbody></table>
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</div>
<ol style="text-align: left;">
<li><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">The fact that interest is a deductible expense
makes debt less expensive than common or preferred stock. As a result, using
debt causes more of the firm’s operating income (EBIT) to flow through to investors.
Therefore, the more debt a company uses, the higher its value of stock prices.
Under the assumptions of the MM(Modigliani and Miller), a firm’s stock price
will be maximized if it uses virtually 100% debt and the line labeled “ MM
result incorporating the Effect of Corporate Taxation” in figure express the
relationship between stock prices and debt under their assumptions.</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">In the real world, firms rarely use 100% debt.
Trade – off theory advocates argue that firms limit their use of debt to hold
down bankruptcy related costs.</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">There is some threshold level of debt , labeled
in figure</span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">a.</span><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: 7pt; text-indent: -0.25in;"> </span></span><br />
<ol style="text-align: left;" type="a"><span style="font-family: 'Trebuchet MS', sans-serif;">
<li><span style="text-indent: -0.25in;"><b>BELOW :</b> The probability of bankruptcy is so low as to be immaterial.b. </span></li>
<li><span style="text-indent: -0.25in;"><b>BEYOND :</b> bankruptcy related cost become increasingly important and they reduce the tax benefits of debt at an increasing rate.c. </span></li>
<li><span style="text-indent: -0.25in;"><b>FROM TO :</b> bankruptcy related costs reduce but do not completely offset the tax benefits of debt, so the stock price rises as the debt ratio increases.d. </span></li>
<li><span style="text-indent: -0.25in;"><b>BEYOND :</b> bankruptcy related costs exceed the tax benefits, so from this point on increasing the debt ratio lowers the value of the stock.</span></li>
</span></ol>
</li>
<li><span class="MsoSubtleReference" style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">Therefore, </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 11pt; line-height: 115%; position: relative; text-indent: -0.25in; top: 4.5pt;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 12pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_79C49F64-0B4A-430D-9080-5C659E7FD6CD.0\msohtmlclip1\01\clip_image002.png">
</v:imagedata></v:shape></span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">is the optimal capital structure. Of course, </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 11pt; line-height: 115%; position: relative; text-indent: -0.25in; top: 4.5pt;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 12pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_79C49F64-0B4A-430D-9080-5C659E7FD6CD.0\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 11pt; line-height: 115%; position: relative; text-indent: -0.25in; top: 4.5pt;"><v:shape id="_x0000_i1025" style="height: 15pt; width: 12pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\Xone\AppData\Local\Temp\OICE_79C49F64-0B4A-430D-9080-5C659E7FD6CD.0\msohtmlclip1\01\clip_image002.png">
</v:imagedata></v:shape></span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">vary firm to firm, depending on their business
risks and bankruptcy costs.</span></li>
<li><span class="MsoSubtleReference" style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">While theoretical and empirical work supports the
general shape of the curves in figure, these graphs must be taken as
approximations, not as precisely defined functions.</span></li>
<li><span class="MsoSubtleReference" style="font-family: 'Trebuchet MS', sans-serif; text-indent: -0.25in;">Another disturbing aspect of capital structure theory
as expressed in figure is the fact that many large successful firms, such as
INTEL and MICROSOFT, use far less debt than the theory suggests.</span></li>
</ol>
<br /></div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-10390696849966856322012-03-24T09:14:00.000-07:002012-03-24T09:15:40.014-07:00CAPITAL STRUCTURE THEORY<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
<br /></div>
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<div style="text-align: justify;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Modern Capital Structure</b> <b>theory</b> began in 1958, when
Professors FRANCO MODIGILANI and MERTON MILLER (hereafter MM) published an
article ” The Cost of Capital ,Corporation Finance and The Theory of
Investment”, what has been called the most influential finance article ever
written.MM proved, under a very restrictive set of assumptions, that a firm’s
value is unaffected by its capital structure. Put another way, MM’s result
suggest that it does not matter how a firm finances its operations, hence
Capital Structure is irrelevant. However, MM’s study was based on some strong
assumptions, including the following:</span><br />
<a name='more'></a><span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
<div style="text-align: justify;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div>
</div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
</div>
<ol style="text-align: left;">
<li style="text-align: justify;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-indent: -0.25in;">There are no brokerage costs.</span></span></li>
<li style="text-align: justify;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-indent: -0.25in;">There are no taxes.</span></span></li>
<li style="text-align: justify;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-indent: -0.25in;">There are no bankruptcy costs.</span></span></li>
<li style="text-align: justify;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-indent: -0.25in;">Investors can borrow at the same rate as
corporations.</span></span></li>
<li style="text-align: justify;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-indent: -0.25in;">All investors have the same information as
management about the firm’s future investment opportunities.</span></span></li>
<li style="text-align: justify;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-indent: -0.25in;">EBIT is not affected by the use of debt.</span></span></li>
</ol>
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span><br />
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><o:p></o:p></span></div>
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<div style="text-align: justify;">
<span style="font-family: 'Trebuchet MS', sans-serif;">Despite the fact that some of these assumptions are obviously
unrealistic, MM’s irrelevance result is extremely important. By indicating the
conditions under which capital structure is irrelevant, MM also provided us
with clues about what is required for capital structure to be relevant and
hence to affect a firm’s value.</span><o:p></o:p></div>
</div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-44868281151579387962012-03-24T07:35:00.001-07:002012-03-24T09:14:35.218-07:00TOP TEN REASONS TO BE AN ACTUARY<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: 'Trebuchet MS', sans-serif;">Why become actuary? Well, it is a usual question arise by every student for every profession. I will try to explain in simple words.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Most actuaries love being actuary because it allows them to use their talents, apply their math skills in a business setting and have a meaningful positive impact. Being an actuary you are helping the people, you are helping them get good health care, you are helping them protect themselves in old age, and you are creating economic growth. But there are other more great reasons to consider a career as an actuary, are as follows:</span><br />
<br />
<a name='more'></a><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Top- Ranked</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">Actuary is considered as one of the best jobs in United States. It is difficult to beat an actuary in work environment, employment outlook, job security, growth opportunity and salary.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Ref :</span><em style="background-color: white; color: #88898a; font-family: AvenirLTStd65Medium, Arial, Helvetica, sans-serif; font-size: 14px; line-height: 21px; text-align: -webkit-auto;">US News and World Report</em><span style="background-color: white; color: #88898a; font-family: AvenirLTStd65Medium, Arial, Helvetica, sans-serif; font-size: 14px; line-height: 21px; text-align: -webkit-auto;">, the </span><em style="background-color: white; color: #88898a; font-family: AvenirLTStd65Medium, Arial, Helvetica, sans-serif; font-size: 14px; line-height: 21px; text-align: -webkit-auto;">Jobs Rated Almanac</em><span style="background-color: white; color: #88898a; font-family: AvenirLTStd65Medium, Arial, Helvetica, sans-serif; font-size: 14px; line-height: 21px; text-align: -webkit-auto;">, </span><em style="background-color: white; color: #88898a; font-family: AvenirLTStd65Medium, Arial, Helvetica, sans-serif; font-size: 14px; line-height: 21px; text-align: -webkit-auto;">CNN Money</em><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Head Start </b>- </span><span style="font-family: 'Trebuchet MS', sans-serif;">Actuaries are consistently rated as one of the best paying jobs in the world. Actuaries earn great starting salaries. Actuaries can start-off with a salary of $20,000 and earn anywhere up to or over $100,000 that can double within the first five years.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Earn while you learn</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">Actuaries are well compensated. Actuary with a fellowship designation working as a financial manager in the banking industry could earn a higher salary than another fellow working in the health insurance industry. Experienced fellows have the potential to earn from <b>$150,000 to $250,000</b> annually and many actuaries earn more than that.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Job Security</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">As you pass the actuarial examinations and gain experience you can award merit increases. They enjoy certainty in uncertain times. Most banks or companies also offer cash bounces, salary increases and promotions for each professional designation achieved.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Impressive Impact - </span><span style="font-family: 'Trebuchet MS', sans-serif;">They participate in high- level business decision making and solve real problems in every banks or industry. Actuaries earn professional degree by passing a series of examinations. These online exams are administered by the <b><a href="http://www.soa.org/" rel="nofollow" target="_blank">SOCIETY OF ACTUARIES</a></b> and <b><a href="http://www.casact.org/" rel="nofollow" target="_blank">CASUALTY ACTUARIAL SOCIETY</a></b>.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Life in Balance</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">Actuaries have a balance between their work and personal life. They have desk jobs and work within a professional office environment. Actuaries often work at least 40 hours a week and may experience a more unpredictable schedule and be expect to work more than 40 hours per week.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Challenging and Stimulating Work</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">The daily work requires a range of skills but the daily work of actuaries is not as demanding as the exams but it is still challenging. A good business sense, an analytical mind, problem solving and independent thinking are all necessary.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>International Career</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">As mentioned above Actuaries are in demanded in United States. Actuaries are particularly in demand in growing economies countries like ASIA. As a fully qualified actuary you would be a very valuable commodity.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>You Get to Work with Models Every Day</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">Actuarial model predict that how many people are going to die within a week? As an actuary you would be using math in most aspect of your work. Being an actuary job, there is a good chance that you have a good aptitude for math.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Well Respected Career</b> - </span><span style="font-family: 'Trebuchet MS', sans-serif;">Actuaries are generally considered to be in the upper echelon of careers along with doctors and lawyers. Qualifies actuaries will have to work hard to get that position. Actuaries are very well respected by those who know what the profession actuary is. </span><br />
<div>
<br /></div>
</div>Anonymoushttp://www.blogger.com/profile/06385476901416370285noreply@blogger.com0tag:blogger.com,1999:blog-6716798511517720994.post-78506982764461277232012-03-22T11:18:00.001-07:002012-03-24T09:14:35.223-07:00IMPORTANCE OF ACTUARIAL SCIENCE AND RISK MANAGEMENT<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>Actuaries</b> are the back bone for the insurance company. Without them, there is no concept of insurance company. They work for insurance companies and predict the profitability of various customers by using the mathematical and statistical formulas. An actuarial degree makes you perfect in Mathematics, Statistics, Economics, Finance and as well as in other subjects of it. After the study of college actuaries spend 5 to 10 years for taking the specialized actuarial exams to become Fellows of the actuarial society. Actuaries estimate the present value cost for future uncertainty like accidents, deaths, natural disaster, disability and lawsuits. Actuaries are engaged in life insurance, retirement benefit consultancies, asset management, post retirement medical benefit, EOBI and provisional social security institutions for the cost of retirement benefit plans. They also involved in periodic valuation of life insurance business, pensions and other investment benefits liabilities. Some fields of actuaries are as follows:</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>BASIC IDEALS:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">With regularly predictable patterns in diseases and life expectancy, it is possible to balance the random events of life and determine a person’s risk to the insurance company. The insurance companies never insure a person who is too risky because they would lose money on that particular person.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>RISK:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Actuary determines the risk that affects the life of person’s life. The main factors are age, disease, likelihood of casualty and other. The “other” factors cover the incidentals of risk that may come person to person.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>NECESSITY:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Without insurance companies it would be very difficult for the average person to survive with catastrophic or random events. Car crashes, plane crashes and natural phenomenon. Insurance companies factor the likelihood of these events into the rates they charge. In the event that something happens the adjusted rates allow them to cover their customers.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>PENSIONS:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">The actuary profession is also vital in determining payouts for pensions. The company would go bankrupt if people were to live too long or the pension payments were too high. So in order that pensions are viable, something that many people depend on. Therefore actuary creates and design the pension plans. They design fair plans that benefit all without leaving the company destitute. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>OTHER TYPES OF INSURANCE:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Actuaries not only to design and creates the plans for life insurance, they are also responsible for certain types of short-term insurance. Short-term insurance are affected by many other factors dealing with people as well as external events.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>SHORT-TERM INSURANCE:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">With life insurance, actuaries calculate the health risks over a lifetime, but in some cases they need to address the short-term risks as well. Actuaries need to be able to factor how changing factors affect a policy over the course of a year. For example: if a crime rate rises significantly, then the insurance company will most likely charge more due to increased risk for someone living in that particular area.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>CRIMINAL SENTENCING:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Some of the time actuaries use to determine the sentences of criminals. This is variables and practices of an actuary. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><b>LIFE, DEATH AND CASUALTIES:</b></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Deaths and casualties are times when a company has to pay the money to the policy holder. Death and casualties are different words. Death is a natural occurrence due to the age factor or disease while casualties are unexpected deaths of individuals. For example: a car wreck or plan crash would be a casualty. Pay the money to the policy holder means that the money is an amount of the life insurance. A $10,000 policy would pay a family $10,000 upon the death or casualties of the holder.</span><br />
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