Exam P Practice Problem 87 – Modeling Insurance Payments

Problem 87-A

A business owner is facing a risk whose economic loss is modeled by the random variable X. The following is the density function of X.

    \displaystyle f(x)=\frac{1}{8} \ (4-x) \ \ \ \ \ \ \ \ 0<x<4

The business owner purchases an insurance policy to cover this potential loss. The insurance policy pays the business owner 80% of the amount of each loss.

Given that a loss has occurred, what is the probability that the amount of the insurance payment to the business owner is less than 2?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   0.25

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   0.36

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   0.64

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   0.75

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   0.86

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Problem 87-B

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

    \displaystyle f(x)=\frac{1}{1800} \ x \ \ \ \ \ \ \ \ 0<x<60

The insurance policy reimburses the policy owner 50% of each loss. Given that a loss has occurred, what is the median amount of the insurance payment made to the policy owner?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 15.00

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 18.65

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 21.21

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 23.63

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 42.43

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Answers

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

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