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dzlab · 2021年03月03日

关于至少有一个人活着的概率计算

NO.PZ2018091705000044

问题如下:

Peter is 79 years old and his wife Lucy is 68 years old. They would like to maintain their living standards with spending requirement of $300,000 in real terms.

Assuming inflation rate is 2% and nominal risk-free rate is 4%. The survival probabilities for the next three years are listed in the following table:

The probability that either Peter or Lucy will survive over the year 1 is:

选项:

A.

0.9197

B.

0.9989

C.

0.9355

解释:

B is correct.

考点:Estimating core capital with mortality tables

解析:表格给出的是每个人每年的存活概率,我们需要计算出至少有一个人存活的概率,即联合概率(joint survival)。

P(jointsurvival)=P(petersurvival+P(LucysurvivalP(petersurvival)×P(Lucysurvival)\begin{array}{l}P(jointsurvival)\\=P(petersurvival+P(Lucysurvival-P(petersurvival)\times P(Lucysurvival)\end{array}\\

所以第一年 P (joint survival) =0.9355+0.9831-0.9355×0.9831=0.9989

我觉得李老师的那个方法有点难理解,就用1-两个都死了的概率就好了
1 个答案

王暄_品职助教 · 2021年03月04日

嗯,你这个想法也挺好的

同学根据你自身决定,哪种好理解,你就用哪个