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Exam C_1106

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Exam C_1106
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  Preliminary Exam C, Fall 2006 ANSWER KEY Question # Answer Question # Answer 1 E 19 B 2 D 20 D 3 B 21 A 4 C 22 A 5 A 23 E 6 D 24 E 7 B 25 D 8 C 26 A 9 E 27 C 10 D 28 C 11 E 29 C 12 B 30 B 13 C 31 C 14 A 32 A 15 B 33 B 16 E 34 A 17 D 35 A 18 D  Exam C: Fall 2006 - 1 - GO ON TO NEXT PAGE   **BEGINNING OF EXAMINATION**   1. You are given: (i)   Losses follow a Burr distribution with α   = 2. (ii)   A random sample of 15 losses is: 195 255 270 280 350 360 365 380 415 450 490 550 575 590 615 (iii)   The parameters γ   and θ   are estimated by percentile matching using the smoothed empirical estimates of the 30 th  and 65 th  percentiles. Calculate the estimate of γ  . (A) Less than 2.9 (B) At least 2.9, but less than 3.2 (C) At least 3.2, but less than 3.5 (D) At least 3.5, but less than 3.8 (E) At least 3.8  Exam C: Fall 2006 - 2 - GO ON TO NEXT PAGE   2. An insurance company sells three types of policies with the following characteristics: Type of Policy Proportion of Total Policies Annual Claim Frequency I 5% Poisson with 0.25 λ   =  II 20% Poisson with 0.50 λ   =  III 75% Poisson with 1.00 λ   =  A randomly selected policyholder is observed to have a total of one claim for Year 1 through Year 4. For the same policyholder, determine the Bayesian estimate of the expected number of claims in Year 5. (A)   Less than 0.4 (B)   At least 0.4, but less than 0.5 (C)   At least 0.5, but less than 0.6 (D)   At least 0.6, but less than 0.7 (E)   At least 0.7  Exam C: Fall 2006 - 3 - GO ON TO NEXT PAGE   3. You are given a random sample of 10 claims consisting of two claims of 400, seven claims of 800, and one claim of 1600. Determine the empirical skewness coefficient. (A)   Less than 1.0 (B)   At least 1.0, but less than 1.5 (C)   At least 1.5, but less than 2.0 (D)   At least 2.0, but less than 2.5 (E)   At least 2.5
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