Exam P Practice Problem 64 – Median Claim Size

Problem 64-A

The following is the density function of the claim size X of an insurance policy from a block of property and casualty insurance policies:

      \displaystyle f(x)=\frac{1}{2} \biggl( 0.4 \ e^{-0.4 x} \biggr) + \frac{1}{2} \biggl( 0.2 \ e^{-0.2 x} \biggr) \ \ \ \ \ \ \ 0<x<\infty

Calculate the median claim size X.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.618

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.739

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.406

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.599

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3.533

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Problem 64-B

The following is the density function of the claim size X of an insurance policy from a block of auto insurance policies:

      \displaystyle f(x)=\frac{3}{4} \biggl( \frac{1}{8} \ x \biggr) + \frac{1}{4} \biggl( \frac{1}{64} \ x^3 \biggr) \ \ \ \ \ \ \ 0<x<4

Calculate the median claim size X.

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.2216

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.4972

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.8653

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.9622

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.9975

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Answers

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