Krzys’ Ostaszewski: http://www.krzysio.net
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Exercise for April 26, 2008
May 2000 Course 1 Examination, Problem No. 24, also Study Note P-09-05, Problem
No. 30
An actuary has discovered that policyholders are three times as likely to file two claims
as to file four claims. If the number of claims filed has a Poisson distribution, what is the
variance of the number of claims filed?
A.
1
3
B. 1
C.
2
D. 2
E. 4
Solution.
Let N be the random number of claims filed. We are given that
e! " " 2
e! " " 4
Pr ( N = 2 ) =
= 3 # Pr ( N = 4 ) = 3 #
.
2!
4!
Therefore, ! 2 = 4 and ! = 2. The variance is the same as the mean and the parameter
! = 2.
Answer D.
© Copyright 2004-2008 by Krzysztof Ostaszewski.
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Exercises from the past actuarial examinations are copyrighted by the Society of
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