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{ }

Answers can be found in this page.

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