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