# 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

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? $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.50$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 0.60$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 0.78$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 1.86$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 2.50$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$

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

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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