Exam P Practice Problem 90 – Insurance Benefits

Problem 90-A

A random loss follows an exponential distribution with mean 20. An insurance reimburses this random loss up to a benefit limit of 30.

When a loss occurs, what is the expected value of the benefit not paid by this insurance policy?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   4.5

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   5.1

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   6.3

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   8.5

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   11.2

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Problem 90-B

A random loss follows an exponential distribution with mean 100. An insurance reimburses this random loss up to a benefit limit of 200.

When a loss occurs, what is the expected value of the benefit not paid by this insurance policy?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   12.6

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   13.5

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   24.6

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   40.6

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   40.7

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Answers

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

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