# Decision theory and probability

May 28th, 2016
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SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETYEXAM C CONSTRUCTION AND EVALUATION OF ACTUARIAL MODELSEXAM C SAMPLE QUESTIONSCopyright 2008 by the Society of Actuaries and the Casualty Actuarial SocietySome of the questions in this study note are taken from past SOA/CAS examinations.C-09-08PRINTED IN U.S.A.1.You are given:(i)Losses follow a loglogistic distribution with cumulative distribution function:bx / gF b xg =1+ bx / g(ii)The sample of losses is:10358086901201581802002101500Calculate the estimate of by percentile matching, using the 40th and 80th empiricallysmoothed percentile estimates.2.(A)Less than 77(B)At least 77, but less than 87(C)At least 87, but less than 97(D)At least 97, but less than 107(E)At least 107You are given:(i)The number of claims has a Poisson distribution.(ii)Claim sizes have a Pareto distribution with parameters = 0.5 and = 6 .(iii)The number of claims and claim sizes are independent.(iv)The observed pure premium should be within 2% of the expected pure premium 90%of the time.Determine the expected number of claims needed for full credibility.(A)Less than 7,000(B)At least 7,000, but less than 10,000(C)At least 10,000, but less than 13,000(D)At least 13,000, but less than 16,000(E)At least 16,000C-09-08-1-3.You study five lives to estimate the time from the onset of a disease to death. The times todeath are:23

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