Course 4 May 2000 Multiple Choice Exams

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16. You are given: (i) x 1 = −2 x 2 = −1 x 3 = 0 x 4 = 1 x 5 = 2 (ii) The true model for the data is y = 10x + 3x 2 + ε . * * . (iii) The model fitted to the data is y = β x + ε Determine the expected value of the least-squares estimator of β * . (A) 6 (B) 7 (C) 8 (D) 9 (E) 10 COURSE/EXAM 4: MAY <strong>2000</strong> - 16 - GO ON TO NEXT PAGE
17. You are given a random sample of two values from a distribution function F: 1 3 b g You estimate θ F X X = + X 2 1 2 . 2 1 = Var b Xg using the estimator g( X1, X2) = ∑ ( Xi − X ) 2 i= 1 2 , where Determine the bootstrap approximation to the mean square error. (A) 0.0 (B) 0.5 (C) 1.0 (D) 2.0 (E) 2.5 COURSE/EXAM 4: MAY <strong>2000</strong> - 17 - GO ON TO NEXT PAGE
Page 1 and 2: **BEGINNING OF EXAMINATION** 1. You
Page 3 and 4: 3. You are given the following info
Page 9 and 10: 9. The following models are fitted
Page 11 and 12: 10-11. (Repeated for convenience) U
Page 13 and 14: 13. You smooth a time series y t us
Page 15: 15. An insurer has data on losses f
Page 19 and 20: 19. For a mortality study with righ
Page 21 and 22: 21. You are given the following fiv
Page 23 and 24: 23. You test the effect of gender a
Page 25 and 26: 25. You model a loss process using
Page 27 and 28: 27. You are analyzing the time betw
Page 29 and 30: 29. You are given the following obs
Page 31 and 32: 31. You fit the following model to
Page 33 and 34: 33. The number of claims a driver h
Page 35 and 36: 35. You fit the following model to
Page 37 and 38: 37. You are given: (i) X i is the c
Page 39 and 40: 39. You fit an AR(1) model to the f
Page 42 and 43: Solutions to May 2000 Course 4 Exam
Page 44 and 45: 11. From pp. 123-5 of KPW and follo
Page 46 and 47: 1 21. Following Example 2.22 on p.
Page 48 and 49: For Actuary 2, the parameters are 2
Page 50: g = 37. From Section 5.4.3 of KPW,

Course 4 May 2000 Multiple Choice Exams

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