coursec_0505 (1) - Exam C May 2005*BEGINNING OF EXAMINATION...

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Exam C: Spring 2005 - 1 - GO ON TO NEXT PAGE **BEGINNING OF EXAMINATION** 1. You are given: (i) A random sample of five observations from a population is: 0.2 0.7 0.9 1.1 1.3 (ii) You use the Kolmogorov-Smirnov test for testing the null hypothesis, 0 H , that the probability density function for the population is: () 5 4 ,0 1 fx x x => + (iii) Critical values for the Kolmogorov-Smirnov test are: Level of Significance 0.10 0.05 0.025 0.01 Critical Value n 22 . 1 n 36 . 1 n 48 . 1 n 63 . 1 Determine the result of the test. (A) Do not reject 0 H at the 0.10 significance level. (B) Reject 0 H at the 0.10 significance level, but not at the 0.05 significance level. (C) Reject 0 H at the 0.05 significance level, but not at the 0.025 significance level. (D) Reject 0 H at the 0.025 significance level, but not at the 0.01 significance level. (E) Reject 0 H at the 0.01 significance level.
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Exam C: Spring 2005 - 2 - GO ON TO NEXT PAGE 2. You are given: (i) The number of claims follows a negative binomial distribution with parameters r and 3 = β . (ii) Claim severity has the following distribution: Claim Size Probability 1 0.4 10 0.4 100 0.2 (iii) The number of claims is independent of the severity of claims. Determine the expected number of claims needed for aggregate losses to be within 10% of expected aggregate losses with 95% probability. (A) Less than 1200 (B) At least 1200, but less than 1600 (C) At least 1600, but less than 2000 (D) At least 2000, but less than 2400 (E) At least 2400
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Exam C: Spring 2005 - 3 - GO ON TO NEXT PAGE 3. You are given: (i) A mortality study covers n lives. (ii) None were censored and no two deaths occurred at the same time. (iii) = k t time of the th k death (iv) A Nelson-Aalen estimate of the cumulative hazard rate function is 380 39 ) ( ˆ 2 = t H . Determine the Kaplan-Meier product-limit estimate of the survival function at time 9 t . (A) Less than 0.56 (B) At least 0.56, but less than 0.58 (C) At least 0.58, but less than 0.60 (D) At least 0.60, but less than 0.62 (E) At least 0.62
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Exam C: Spring 2005 - 4 - GO ON TO NEXT PAGE 4. Three observed values of the random variable X are: 1 1 4 You estimate the third central moment of X using the estimator: () 3 123 1 ,, 3 i gX X X X X =− Determine the bootstrap estimate of the mean-squared error of g . (A) Less than 3.0 (B) At least 3.0, but less than 3.5 (C) At least 3.5, but less than 4.0 (D) At least 4.0, but less than 4.5 (E) At least 4.5
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Exam C: Spring 2005 - 5 - GO ON TO NEXT PAGE 5. You are given the following p - p plot: 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 F n (x) F(x) The plot is based on the sample: 1 2 3 15 30 50 51 99 100 Determine the fitted model underlying the p - p plot. (A) F( x ) = 1 – 0.25 x , x 1 (B) F( x ) = x / (1 + x ), x 0 (C) Uniform on [1, 100] (D) Exponential with mean 10 (E) Normal with mean 40 and standard deviation 40
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Exam C: Spring 2005 - 6 - GO ON TO NEXT PAGE 6. You are given: (i) Claims are conditionally independent and identically Poisson distributed with mean Θ . (ii) The prior distribution function of Θ is: 2.6 1 () 1 1 F θ ⎛⎞ =− ⎜⎟ + ⎝⎠ , 0 > Five claims are observed.
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This note was uploaded on 11/14/2011 for the course MAT 2070 taught by Professor S.g. during the Spring '11 term at Université du Québec à Montréal.

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coursec_0505 (1) - Exam C May 2005*BEGINNING OF EXAMINATION...

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