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Unformatted text preview: Course 4: May 2001  1  GO ON TO NEXT PAGE May, 2001 Society of Actuaries **BEGINNING OF EXAMINATION** 1. You are given the following information about an invertible ARMA timeseries model: r r 1 0 4 2 3 4 =  = = . , , , ,... k k Determine q 1 . (A) 0.2 (B) 0.3 (C) 0.4 (D) 0.5 (E) 0.6 Course 4: May 2001  2  GO ON TO NEXT PAGE 2. You are given: (i) Annual claim counts follow a Poisson distribution with mean l . (ii) The parameter l has a prior distribution with probability density function: f e l l l b g = 1 3 3 , Two claims were observed during the first year. Determine the variance of the posterior distribution of l . (A) 9/16 (B) 27/16 (C) 9/4 (D) 16/3 (E) 27/4 Course 4: May 2001  3  GO ON TO NEXT PAGE 34. Use the following information for questions 3 and 4. You are given the following times of first claim for five randomly selected auto insurance policies observed from time t = 0: 1 2 3 4 5 3 . Calculate the kurtosis of this sample. (A) 0.0 (B) 0.5 (C) 1.7 (D) 3.4 (E) 6.8 Course 4: May 2001  4  GO ON TO NEXT PAGE 34. (Repeated for convenience) Use the following information for questions 3 and 4. You are given the following times of first claim for five randomly selected auto insurance policies observed from time t = 0: 1 2 3 4 5 4. You are later told that one of the five times given is actually the time of policy lapse, but you are not told which one. The smallest ProductLimit estimate of S (4), the probability that the first claim occurs after time 4, would result if which of the given times arose from the lapsed policy? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Course 4: May 2001  5  GO ON TO NEXT PAGE 5. A professor ran an experiment in three sections of a psychology course to show that the more digits in a number, the more difficult it is to remember. The following variables were used in a multiple regression: X 2 = number of digits in the number X 3 = 1 if student was in section 1, 0 otherwise X 4 = 1 if student was in section 2, 0 otherwise Y = percentage of students correctly remembering the number You are given: (i) A total of 42 students participated in the study. (ii) The regression equation Y X X X X = + + + + + b b b b b e 1 2 2 3 2 2 4 3 5 4 was fit to the data and resulted in R 2 0940 = . . (iii) A second regression equation Y X X = + + + g g g e 1 2 2 3 2 2 * was fit to the data and resulted in R 2 0915 = . . Determine the value of the F statistic used to test whether class section is a significant variable. (A) 5.4 (B) 7.3 (C) 7.7 (D) 7.9 (E) 8.3 Course 4: May 2001  6  GO ON TO NEXT PAGE 6. You are given: (i) The full credibility standard is 100 expected claims. (ii) The squareroot rule is used for partial credibility. You approximate the partial credibility formula with a Bühlmann credibility formula by selecting a Bühlmann k value that matches the partial credibility formula when 25 claims are expected....
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 Spring '12
 ZhangQiang
 Normal Distribution, Variance, di Yi Yi

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