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Unformatted text preview: Course 4: November 20011 GO ON TO NEXT PAGE November 2001 Course 4 Society of Actuaries **BEGINNING OF EXAMINATION** 1. For a secondorder autoregressive process, you are given: r 1 053 = . r 2 022 =  . Determine r 3 . (A) Less than –0.70 (B) At least –0.70, but less than –0.30 (C) At least –0.30, but less than 0.10 (D) At least 0.10, but less than 0.50 (E) At least 0.50 Course 4: November 20012 GO ON TO NEXT PAGE 2. You are given: Claim Size Number of Claims 025 30 2550 32 50100 20 100200 8 Assume a uniform distribution of claim sizes within each interval. Estimate the second raw moment of the claim size distribution. (A) Less than 3300 (B) At least 3300, but less than 3500 (C) At least 3500, but less than 3700 (D) At least 3700, but less than 3900 (E) At least 3900 Course 4: November 20013 GO ON TO NEXT PAGE 3. You are given: (i) The number of claims per auto insured follows a Poisson distribution with mean l . (ii) The prior distribution for l has the following probability density function: f e l l l l b g b g b g = 500 50 50 500 Γ (iii) A company observes the following claims experience: Year 1 Year 2 Number of claims 75 210 Number of autos insured 600 900 The company expects to insure 1100 autos in Year 3. Determine the expected number of claims in Year 3. (A) 178 (B) 184 (C) 193 (D) 209 (E) 224 Course 4: November 20014 GO ON TO NEXT PAGE 4. Which of the following statements about the ProductLimit estimator is false? (A) The ProductLimit estimator is based on the assumption that knowledge of a censoring time for an individual provides no further information about this person’s likelihood of survival at a future time had the individual continued in the study. (B) If the largest study time corresponds to a death time, then the ProductLimit estimate of the survival function is undetermined beyond this death time. (C) When there is no censoring or truncation, the ProductLimit estimator reduces to the empirical survival function. (D) Under certain regularity conditions, the ProductLimit estimator is a nonparametric maximum likelihood estimator. (E) The ProductLimit estimator is consistent. Course 4: November 20015 GO ON TO NEXT PAGE 5. You fit the following model to eight observations: Y X = + + a b e You are given: $ . . $ b =  = = ∑ ∑ 3569 162 2394 2 2 X X Y Y i i i c h d i Determine the symmetric 90percent confidence interval for b . (A) (–74.1, 2.7) (B) (–66.2, –5.2) (C) (–63.2, –8.2) (D) (–61.5, –9.9) (E) (–61.0, –10.4) Course 4: November 20016 GO ON TO NEXT PAGE 6. The graph below shows a qq plot of a fitted distribution compared to a sample. Sample Which of the following is true? (A) The tails of the fitted distribution are too thick on the left and on the right, and the fitted distribution has less probability around the median than the sample....
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 Spring '12
 ZhangQiang

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