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<x<10 \\           \text{ } & \text{ } \\           0 &\ \ \ \ \ \ x \ge 10           \end{array} \right.

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

\text{ }

      \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.

\text{ }

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

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

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

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

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

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probability exam P

actuarial exam

math

Daniel Ma

mathematics

Answers

\copyright 2017 – Dan Ma

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