# Exam P Practice Problem 59 – Joint Distributions

Problem 59-A

Two random losses $X$ and $Y$ are jointly modeled by the following density function: $\displaystyle f(x,y)=\frac{1}{32} \ (4-x) \ (4-y) \ \ \ \ \ \ 0

Suppose that both of these losses had occurred. Given that $X$ exceeds 2, what is the probability that $Y$ is less than 2? $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.4000$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.4667$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.7518$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.8571$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.9375$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$

Problem 59-B

Two random losses $X$ and $Y$ are jointly modeled by the following density function: $\displaystyle f(x,y)=\frac{1}{96} \ (x+2y) \ \ \ \ \ \ 0

Suppose that both of these losses had occurred. What is the probability that only one of them exceeds 2? $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.1250$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.2083$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.2917$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.3750$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.5000$

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Answers

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