Course4_1101.PDF - Course 4: November 2001-1- GO ON TO NEXT...

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Unformatted text preview: Course 4: November 2001-1- GO ON TO NEXT PAGE November 2001- Course 4 Society of Actuaries **BEGINNING OF EXAMINATION** 1. For a second-order 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 2001-2- GO ON TO NEXT PAGE 2. You are given: Claim Size Number of Claims 0-25 30 25-50 32 50-100 20 100-200 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 2001-3- 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 2001-4- GO ON TO NEXT PAGE 4. Which of the following statements about the Product-Limit estimator is false? (A) The Product-Limit 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 Product-Limit estimate of the survival function is undetermined beyond this death time. (C) When there is no censoring or truncation, the Product-Limit estimator reduces to the empirical survival function. (D) Under certain regularity conditions, the Product-Limit estimator is a nonparametric maximum likelihood estimator. (E) The Product-Limit estimator is consistent. Course 4: November 2001-5- 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 90-percent 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 2001-6- GO ON TO NEXT PAGE 6. The graph below shows a q-q 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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Course4_1101.PDF - Course 4: November 2001-1- GO ON TO NEXT...

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