# Exam P Practice Problem 54 – Expected Insurance Payment

Problem 54-A

An insurance policy is purchased to reimburse a loss that is modeled by the following probability density function:

$\displaystyle f(x)=\frac{30}{1024} \ x^2 \ (4-x)^2 \ \ \ \ \ \ \ 0

This insurance policy has a deductible of 1 with an additional provision that any loss that exceeds the deductible will be paid in full to the policyholder.

When there is a loss, what is the expected amount paid to the policyholder under this policy?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 1.028$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 1.598$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 1.836$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 1.925$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 2.000$

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Problem 54-B

An insurance policy is purchased to reimburse a loss that is modeled by the following probability density function:

$\displaystyle f(x)=\frac{5}{256} \ x^3 \ (4-x) \ \ \ \ \ \ \ 0

This insurance policy has a deductible of 2 with an additional provision that any loss that exceeds the deductible will be paid in full to the policyholder.

When there is a loss, what is the expected amount paid to the policyholder under this policy?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 0.750$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 2.375$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 2.667$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 3.375$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 3.667$

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