Exam P Practice Problem 92 – Expected Claim Payment

Problem 92-A

The size of a claim that an auto insurance company pays out is modeled by a random variable with the following density function:

    \displaystyle f(x)=\frac{1}{5000} \ (100-x) \ \ \ \ \ \ \ 0<x<100

By subjecting the insured to a deductible of 12 per claim, what is the expected reduction in claim payment?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   9.50

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   10.6

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   11.1

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   11.8

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   12.0

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Problem 92-B

The size of a claim that an auto insurance company pays out is modeled by a random variable with the following density function:

    \displaystyle f(x)=\frac{1}{3200} \ (80-x) \ \ \ \ \ \ \ 0<x<80

By subjecting the insured to a deductible of 10 per claim, by what percent is the expected claim payment reduced?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   10 \%

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   15 \%

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   22 \%

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   25 \%

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   33 \%

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Answers

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\copyright \ 2015 \ \ \text{ Dan Ma}

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