Exam P Practice Problem 93 – Determining Average Claim Frequency

Problem 93-A

An actuary performs a claim frequency study on a group of auto insurance policies. She finds that the probability function of the number of claims per week arising from this set of policies is P(N=n) where n=1,2,3,\cdots. Furthermore, she finds that P(N=n) is proportional to the following function:

    \displaystyle \frac{e^{-2.9} \cdot 2.9^n}{n!} \ \ \ \ \ \ \ n=1,2,3,\cdots

What is the weekly average number of claims arising from this group of insurance policies?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   2.900

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   3.015

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   3.036

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   3.069

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   3.195

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Problem 93-B

Let N be the number of taxis arriving at an airport terminal per minute. It is observed that there are at least 2 arrivals of taxis in each minute. Based on a study performed by a traffic engineer, the probability P(N=n) is proportional to the following function:

    \displaystyle \frac{e^{-2.9} \cdot 2.9^n}{n!} \ \ \ \ \ \ \ n=2,3,4,\cdots

What is the average number of taxis arriving at this airport terminal per minute?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   2.740

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   2.900

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   3.339

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   3.489

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   3.692

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Answers

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\copyright \ 2015 \ \ \text{ Dan Ma}

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