# Exam P Practice Problem 25 – Uniform Distribution

__________________________________________________________________
This post has no alternate problem. It has one problem with 3 parts.

Problem 25

A real estate property owner is at risk for losses due to two different perils affecting her property. There are no other potential losses in addition to these two different types of losses. Let $X$ be the total amount of the losses in a year due to one peril and let $Y$ be the total amount of the losses in a year due to the other peril. Suppose that $X$ and $Y$ are independent and are identically and uniformly distributed from $0$ to $10$.

In recent years, the owner finds that the total annual losses (due to both perils) always exceed 10.

1. What is the probability that the loss $X$ exceeds $5$?
2. What is the expected annual loss $X$?
3. What is the variance of the annual loss $X$?

__________________________________________________________________

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

$\text{ }$

__________________________________________________________________

$\copyright \ 2013$