Unformatted text preview: Name: A ﬁﬂjuﬁﬂ 9’7 UNIVERSITY OF ILLINOIS AT URBANA—CHAMPAIGN
Actuarial Science Program
DEPARTMENT OF MATHEMATICS Math 478/ 568 Prof. Rick Gorvett
Actuarial Modeling Spring 2009 InClass Assignment # 3 (2 problems worth 1 point each)
Tuesday, February 3, 2009 This assignment is open—book, opennote, and you may work together in groups of no more than
4. Each student must hand in her/his own answer sheet. Please circle your ﬁnal answers. Both
the ﬁnal answer and the method must be correct to achieve full credit. (1) A claim count distribution can be expressed as a mixed Poisson distribution. The mean of
the Poisson distribution is uniformly distributed over the interval [0,4]. Calculate the probability that there are zero claims.
l V >~
Vﬂ‘ ﬂtx = T e
0 PD): '03= S: L: e q‘l’l /
u’ 1. : ﬂ '5‘.
.. [email protected] H) o ‘f 0.243 on. 2"] (2) You are given:
(i) The claim count N has a Poisson distribution with mean A .
(ii) A has an unknown distribution with a mean of 2 and a variance of 7.
Calculate the coefﬁcient of variation of N. £M=E[€(UIA)] = EfA] =2 Vanish = Elwin (Ml4)) ‘l' \laa [ﬂu/AD
ETA] 4" VAan} :2“) :3 CA): 0..” :F/ ...
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 Spring '09
 Gorvett

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