# Exam P Practice Problem 61 – Claim Size of Auto Insurance Policies

Problem 61-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 an exponential distribution with mean 1.25.

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

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

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ 1563$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ 2500$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ 2755$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ 3125$

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Problem 61-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 an exponential distribution with mean 1.6.

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

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ 1600$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ 5120$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ 9756.43$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ 11448.67$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ 12541.39$

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