# 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?

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

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

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

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

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

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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

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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