# 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?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.1250$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 0.2083$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 0.2917$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 0.3750$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 0.5000$

____________________________________________________

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

____________________________________________________

$\copyright \ 2013$