# Exam P Practice Problem 43 – Joint Random Losses

Problem 43-A

Two random losses $X$ and $Y$ are jointly distributed according to the following density function:

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

Suppose that these two random losses had occurred. If the total loss is 5, what is the expected value of the loss $X$?

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Problem 43-B

Two random losses $X$ and $Y$ are jointly distributed according to the following density function:

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

Suppose that these two random losses had occurred. If the total loss is 6, what is the expected value of the loss $X$?

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