# 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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Answers

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### 3 responses

1. I don’t understand why the answer is not zero. The distribution is continuous and we are finding the value at an exact point.

1. Never mind, on closer inspection it makes since, we are looking at what percentage x has at that point, which since the distribution is symmetrical is a half or 2.5 and 3 respectively.

2. […] Several practice problems that closely match the topics discussed in this post are problem 104, problem 43, problem 32 and problem […]