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 1.00 (D) At least 1.00, but less than 1.25 (E) At least 1.25
Exam C: Fall 2005-2-GO ON TO NEXT PAGE2. You are given: (i) The conditional distribution of the number of claims per policyholder is Poisson with mean λ. (ii) The variable λhas a gamma distribution with parameters αand θ. (iii) For policyholders with 1 claim in Year 1, 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, the credibility estimate for the number of claims in Year 3 is 0.20. Determine θ.
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Exam C: Fall 2005-3-GO ON TO NEXT PAGE3.A random sample of claims has been drawn from a Burr distribution with known parameter α= 1 and unknown parameters θand 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 θby percentile matching. (A) Less than 190 (B) At least 190, but less than 200 (C) At least 200, but less than 210 (D) At least 210, but less than 220 (E) At least 220