Exam P Practice Problem 55 – Expected Benefit Payment

Problem 55-A

The following is the joint density function of two random losses X and Y.

      \displaystyle f(x,y)=\frac{3}{16} \ x^2 \ \ \ \ \ \ \ \ \ 0<x<2, \ 0<y<2

An insurance policy is purchased to cover the total loss X+Y subject to a deductible of 2.

When the losses X and Y occur, what is the expected benefit paid by this insurance policy?

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

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 0.60

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 0.78

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 1.86

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 2.50

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Problem 55-B

The following is the joint density function of two random losses X and Y.

      \displaystyle f(x,y)=\frac{1}{64} \ x \ y \ \ \ \ \ \ \ \ \ 0<x<4, \ 0<y<4

An insurance policy is purchased to cover the total loss X+Y subject to a deductible of 4.

When the losses X and Y occur, what is the expected benefit paid by this insurance policy?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 5.333

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 1.833

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 1.333

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 1.467

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 1.296

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Answers

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\copyright \ 2013

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