# Exam P Practice Problem 97 – Variance of Claim Sizes

Problem 97-A

For a type of insurance policies, the following is the probability that the size of claim is greater than $x$.

$\displaystyle P(X>x) = \left\{ \begin{array}{ll} \displaystyle 1 &\ \ \ \ \ \ x \le 0 \\ \text{ } & \text{ } \\ \displaystyle \biggl(1-\frac{x}{10} \biggr)^6 &\ \ \ \ \ \ 0

Calculate the variance of the claim size for this type of insurance policies.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \frac{10}{7}$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \frac{75}{49}$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \frac{95}{49}$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \frac{15}{7}$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \frac{25}{7}$

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Problem 97-B

For a type of insurance policies, the following is the probability that the size of a claim is greater than $x$.

$\displaystyle P(X>x) = \left\{ \begin{array}{ll} \displaystyle 1 &\ \ \ \ \ \ x \le 0 \\ \text{ } & \text{ } \\ \displaystyle \biggl(\frac{250}{x+250} \biggr)^{2.25} &\ \ \ \ \ \ x>0 \\ \end{array} \right.$

Calculate the expected claim size for this type of insurance policies.

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 200.00$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 203.75$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 207.67$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 217.32$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 232.74$

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