Mathematics: Two life insurance policies, each with a death benefit of 10,000 and a one-time premium of 500, are sold to a couple, one for each person. the policies will expire at the end of the tenth year. the probability that only the wife will survive at least ten years is 0.025, the probability that only the husband will survive at least ten years is 0.01, and the probability that both of them will survive at least ten years is 0.96 . what is the expected excess of premiums over claims, given that the husband

Two life insurance policies, each with a death benefit

Ответ:

swelch2010

02.01.2022

Mathematics

896.9

Step-by-step explanation:

Let x denotes excess premium over claims

$E\left ( x|husband survives\right )$ , There are two possibilities

(i)Only husband survives

This can be possible with a possibility of 0.01

Claims=10,000

Premium collected $=2\times 500=1000$

Thus x=1000-10,000=-9000

(ii)Both husband and wife survives

This can occur with a probability of 0.96

Here claims will be 0 as both survives

Premium taken=1000

thus x=1000

The probability that the husband survives is the sum of above cases

=0.96+0.01=0.97

Hence the desired conditional Expectation $E\left ( x|Husband survives\right ) =0.01\times \left ( -9000\right )+0.96\times \left ( 1000\right )=896.9$

0,0(0 оценок)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question