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# ica3 - Name A ﬁﬂjuﬁﬂ 9’7 UNIVERSITY OF ILLINOIS...

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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 In-Class Assignment # 3 (2 problems worth 1 point each) Tuesday, February 3, 2009 This assignment is open—book, open-note, 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 (Ml-4)) ‘l' \laa [ﬂu/AD ETA] 4" VAan} :2“) :3 CA): 0..” :F/ ...
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