Exam P Practice Problem 88 – Expected Value of Insurance Payments

Problem 88-A

A random loss X has a uniform distribution over the interval 0<x<20. An insurance policy is purchased to reimburse the loss up to a maximum limit of m where 0<m<20.

The expected value of the benefit payment under this policy is 8.4. Calculate the value of m.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   8.7

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   9.0

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   12.0

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   13.6

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   18.3

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Problem 88-B

An individual purchases an insurance policy to cover a loss X whose density function is:

    \displaystyle f(x)=\frac{2}{25} \ (5-x) \ \ \ \ \ \ \ \ 0<x<5

The insurance policy reimburses the policy owner up to a benefit limit of 4 for each loss. What is the expected value of insurance payment made to the policy owner?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 1.35

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 1.41

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 1.49

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 1.65

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 1.67

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Answers

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\copyright \ 2014 \ \ \text{ Dan Ma}

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