edu-2008-spring-c-questions

# edu-2008-spring-c-questions - SOCIETY OF ACTUARIES/CASUALTY...

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SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM C CONSTRUCTION AND EVALUATION OF ACTUARIAL MODELS EXAM C SAMPLE QUESTIONS Copyright 2008 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study note are taken from past SOA/CAS examinations. C-09-08 PRINTED IN U.S.A.

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C-09-08 - 1 - 1. You are given: (i) Losses follow a loglogistic distribution with cumulative distribution function: Fx x x bg = + / / θ γ 1 (ii) The sample of losses is: 10 35 80 86 90 120 158 180 200 210 1500 Calculate the estimate of by percentile matching, using the 40 th and 80 th empirically smoothed percentile estimates. (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 107 2. You are given: (i) The number of claims has a Poisson distribution. (ii) Claim sizes have a Pareto distribution with parameters = 0.5 and α = 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 16,000
C-09-08 - 2 - 3. You study five lives to estimate the time from the onset of a disease to death. The times to death are: 2 3 3 3 7 Using a triangular kernel with bandwidth 2, estimate the density function at 2.5. (A) 8/40 (B) 12/40 (C) 14/40 (D) 16/40 (E) 17/40 4. You are given: (i) Losses follow a Single-parameter Pareto distribution with density function: () 1 ,1 f xx x α + = > , 0 < < (ii) A random sample of size five produced three losses with values 3, 6 and 14, and two losses exceeding 25. Determine the maximum likelihood estimate of . (A) 0.25 (B) 0.30 (C) 0.34 (D) 0.38 (E) 0.42

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C-09-08 - 3 - 5. You are given: (i) The annual number of claims for a policyholder has a binomial distribution with probability function: () () 2 2 1 x x pxq q q x ⎛⎞ =− ⎜⎟ ⎝⎠ , x = 0, 1, 2 (ii) The prior distribution is: () 3 4, 0 1 qq q π = << This policyholder had one claim in each of Years 1 and 2. Determine the Bayesian estimate of the number of claims in Year 3. (A) Less than 1.1 (B) At least 1.1, but less than 1.3 (C) At least 1.3, but less than 1.5 (D) At least 1.5, but less than 1.7 (E) At least 1.7 6. For a sample of dental claims 12 1 0 , ,..., x xx , you are given: (i) 2 3860 and 4,574,802 ii == ∑∑ (ii) Claims are assumed to follow a lognormal distribution with parameters μ and σ . (iii) and are estimated using the method of moments. Calculate EX 500 for the fitted distribution. (A) Less than 125 (B) At least 125, but less than 175 (C) At least 175, but less than 225 (D) At least 225, but less than 275 (E) At least 275
C-09-08 - 4 - 7. DELETED 8. You are given: (i) Claim counts follow a Poisson distribution with mean θ . (ii) Claim sizes follow an exponential distribution with mean 10 . (iii) Claim counts and claim sizes are independent, given .

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edu-2008-spring-c-questions - SOCIETY OF ACTUARIES/CASUALTY...

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