Monthly Archives: April, 2016

Exam P Practice Problem 96 – Expected Insurance Payment

Problem 96-A

An insurance policy is purchased to cover a random loss subject to a deductible of 1. The cumulative distribution function of the loss amount X is:

    \displaystyle  F(x) = \left\{ \begin{array}{ll}           \displaystyle  0 &\ \ \ \ \ \ x<0 \\            \text{ } & \text{ } \\          \displaystyle  \frac{3}{25} \ x^2 - \frac{2}{125} \ x^3 &\ \ \ \ \ \ 0 \le x<5 \\           \text{ } & \text{ } \\           1 &\ \ \ \ \ \ 5<x           \end{array} \right.

Given a random loss X, determine the expected payment made under this insurance policy?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.50

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 1.54

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 1.72

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 4.63

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 6.26

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Problem 96-B

An insurance policy is purchased to cover a random loss subject to a deductible of 2. The density function of the loss amount X is:

    \displaystyle  f(x) = \left\{ \begin{array}{ll}                     \displaystyle  \frac{3}{8} \biggl(1- \frac{1}{4} \ x + \frac{1}{64} \ x^2 \biggr) &\ \ \ \ \ \ 0<x<8 \\           \text{ } & \text{ } \\           0 &\ \ \ \ \ \ \text{otherwise}           \end{array} \right.

Given a random loss X, what is the expected benefit paid by this insurance policy?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.51

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 0.57

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 0.63

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 1.60

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 2.00

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Answers

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\copyright \ 2016 - \text{Dan Ma}

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