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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Answers

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

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