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(Created page with "'''Answer: E''' From the SULT, we have: <math display="block"> \begin{aligned} { }_{25} p_{20} & =\frac{l_{45}}{l_{20}}=\frac{99,033.9}{100,000.0}=0.99034 \\ { }_{25} p_{45} & =\frac{l_{70}}{l_{45}}=\frac{91,082.4}{99,033.9}=0.91971 \end{aligned} </math> The expected number of survivors from the sons is 1980.68 with variance 19.133. The expected number of survivors from fathers is 1839.42 with variance 147.687. The total expected number of survivors is therefore...") |
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The <math>99^{\text {th }}</math> percentile equals <math>3820.10+(2.326)(12.916)=3850</math> | The <math>99^{\text {th }}</math> percentile equals <math>3820.10+(2.326)(12.916)=3850</math> | ||
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Revision as of 02:33, 18 January 2024
Answer: E
From the SULT, we have:
[[math]]
\begin{aligned}
{ }_{25} p_{20} & =\frac{l_{45}}{l_{20}}=\frac{99,033.9}{100,000.0}=0.99034 \\
{ }_{25} p_{45} & =\frac{l_{70}}{l_{45}}=\frac{91,082.4}{99,033.9}=0.91971
\end{aligned}
[[/math]]
The expected number of survivors from the sons is 1980.68 with variance 19.133.
The expected number of survivors from fathers is 1839.42 with variance 147.687.
The total expected number of survivors is therefore 3820.10 .
The standard deviation of the total expected number of survivors is therefore
[[math]]
\sqrt{19.133+147.687}=\sqrt{166.82}=12.916
[[/math]]
The [math]99^{\text {th }}[/math] percentile equals [math]3820.10+(2.326)(12.916)=3850[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.