# Exam P Practice Problem 102 – estimating claim costs

Problem 102-A

Insurance claims modeled by a distribution with the following cumulative distribution function. $\displaystyle F(x) = \left\{ \begin{array}{ll} \displaystyle 0 &\ \ \ \ \ \ x \le 0 \\ \text{ } & \text{ } \\ \displaystyle \frac{1}{1536} \ x^4 &\ \ \ \ \ \ 0 < x \le 4 \\ \text{ } & \text{ } \\ \displaystyle 1-\frac{2}{3} x+\frac{1}{8} x^2- \frac{1}{1536} \ x^4 &\ \ \ \ \ \ 4 < x \le 8 \\ \text{ } & \text{ } \\ \displaystyle 1 &\ \ \ \ \ \ x > 8 \\ \end{array} \right.$

The insurance company is performing a study on all claims that exceed 3. Determine the mean of all claims being studied. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 4.8$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 4.9$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 5.0$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 5.1$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 5.2$ $\text{ }$ $\text{ }$ $\text{ }$

Problem 102-B

Insurance claims modeled by a distribution with the following cumulative distribution function. $\displaystyle F(x) = \left\{ \begin{array}{ll} \displaystyle 0 &\ \ \ \ \ \ x \le 0 \\ \text{ } & \text{ } \\ \displaystyle \frac{1}{50} \ x^2 &\ \ \ \ \ \ 0 < x \le 5 \\ \text{ } & \text{ } \\ \displaystyle -\frac{1}{50} x^2+\frac{2}{5} x- 1 &\ \ \ \ \ \ 5 < x \le 10 \\ \text{ } & \text{ } \\ \displaystyle 1 &\ \ \ \ \ \ x > 10 \\ \end{array} \right.$

The insurance company is performing a study on all claims that exceed 4. Determine the mean of all claims being studied. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 5.9$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 6.0$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 6.1$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 6.2$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 6.3$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$

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