# Exam P Practice Problem 83 – Claim Size of Auto Insurance Policies

Problem 83-A

An insurance company has a block of auto insurance policies. The claim size (in thousands) for a policy in this block of auto insurance policies is modeled by the random variable $Y=X^2$ where $X$ has a normal distribution with mean 0 and variance 1.5.

What is the expected claim size for such an auto insurance policy?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ 1250$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ 1500$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ 1750$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ 2250$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ 2500$

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Problem 83-B

An insurance company has a block of auto insurance policies. The claim size (in thousands) for a policy in this block of auto insurance policies is modeled by the random variable $Y=X^2$ where $X$ has a normal distribution with mean 0 and variance 3.

What is the standard deviation of the claim size for such an auto insurance policy?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ 1732$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ 3000$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ 4243$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ 4987$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ 5732$

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$\copyright \ 2014 \ \ \text{Dan Ma}$