Monthly Archives: October, 2015

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}

Exam P Practice Problem 92 – Expected Claim Payment

Problem 92-A

The size of a claim that an auto insurance company pays out is modeled by a random variable with the following density function:

    \displaystyle f(x)=\frac{1}{5000} \ (100-x) \ \ \ \ \ \ \ 0<x<100

By subjecting the insured to a deductible of 12 per claim, what is the expected reduction in claim payment?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   9.50

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   10.6

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   11.1

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   11.8

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   12.0

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Problem 92-B

The size of a claim that an auto insurance company pays out is modeled by a random variable with the following density function:

    \displaystyle f(x)=\frac{1}{3200} \ (80-x) \ \ \ \ \ \ \ 0<x<80

By subjecting the insured to a deductible of 10 per claim, by what percent is the expected claim payment reduced?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \   10 \%

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \   15 \%

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \   22 \%

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \   25 \%

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \   33 \%

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