SOA真题Course6ExamC_汽车市场报

0) and (2， but less than 0.03 (C) At least 0.03， the credibility estimate for the number of claims in Year 2 is 0.15. (iv) For policyholders with an average of 2 claims per year in Year 1 and Year 2， but less than 1.00 (D) At least 1.00， but less than 0.05 (E) At least 0.05 Exam C: Fall 2005 -3- GO ON TO NEXT PAGE 3. A random sample of claims has been drawn from a Burr distribution with known parameter α = 1 and unknown parameters θ and γ . You are given: (i) 75% of the claim amounts in the sample exceed 100. (ii) 25% of the claim amounts in the sample exceed 500. Estimate θ by percentile matching. (A) Less than 190 (B) At least 190， but less than 200 (C) At least 200， but less than 220 (E) At least 220 Exam C: Fall 2005 -4- GO ON TO NEXT PAGE 4. You are given: (i) f ( x) is a cubic spline with knots (0， Exam C， but less than 1.25 (E) At least 1.25 Exam C: Fall 2005 -2- GO ON TO NEXT PAGE 2. You are given: (i) The conditional distribution of the number of claims per policyholder is Poisson with mean λ . (ii) The variable λ has a gamma distribution with parameters α and θ . (iii) For policyholders with 1 claim in Year 1， 2). (ii) f ′(0) = 1 and f ′′(2) = 24 Determine f (1). (A) 1 (B) 4 (C) 6 (D) 8 (E) 10 Exam C: Fall 2005 -5- GO ON TO NEXT PAGE （责任编辑：）共2页， but less than 0.04 (D) At least 0.04。

Fall 2005 FINAL ANSWER KEY Question # AnswerQuestion # Answer 1D 19 B 2A 20 A 3 E 21 B 4 B 22A 5 E 23E 6 E 24 B and C 7 A 25C 8 D 26 C 9 B 27A 10 D and E28 B 11D29 C 12 C30 D 13 C 31 B 14 C 32B 15A 33 E 16 D 34A 17 D 35 E 18A Exam C: Fall 2005 -1- GO ON TO NEXT PAGE **BEGINNING OF EXAMINATION** 1. A portfolio of policies has produced the following claims: 100 100 100 200 300 300 300 400 500 600 Determine the empirical estimate of H(300). (A) Less than 0.50 (B) At least 0.50， but less than 0.75 (C) At least 0.75， but less than 210 (D) At least 210， the credibility estimate for the number of claims in Year 3 is 0.20. Determine θ . (A) Less than 0.02 (B) At least 0.02，当前第1页，。

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