edu-mc-exam-c-0507 - *BEGINNING OF EXAMINATION* 1. For a...

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Exam C: Spring 2007 - 1 - GO ON TO NEXT PAGE **BEGINNING OF EXAMINATION** 1. For a dental policy, you are given: (i) Ground-up losses follow an exponential distribution with mean θ . (ii) Losses under 50 are not reported to the insurer. (iii) For each loss over 50, there is a deductible of 50 and a policy limit of 350. (iv) A random sample of five claim payments for this policy is: 50 150 200 350 + 350 + where + indicates that the original loss exceeds 400. Determine the likelihood function ( ) L . (A) 1100 5 1 e (B) 1300 5 1 e (C) 1350 5 1 e (D) 1100 3 1 e (E) 1350 3 1 e
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Exam C: Spring 2007 - 2 - GO ON TO NEXT PAGE 2. For a group of risks, you are given: (i) The number of claims for each risk follows a binomial distribution with parameters 6 m = and q . (ii) The values of q range from 0.1 to 0.6. During Year 1, k claims are observed for a randomly selected risk. For the same risk, both Bayesian and Bühlmann credibility estimates of the number of claims in Year 2 are calculated for 0,1,2,. ..,6 k = . Determine the graph that is consistent with these estimates. (A) (B) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0123456 Year 1 Claims Estimated Year 2 Claims Bühlmann Bayesian 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Year 1 Claims Bühlmann Bayesian
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Exam C: Spring 2007 - 3 - GO ON TO NEXT PAGE 2. (Continued) (C) (D) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0123456 Year 1 Claims Estimated Year 2 Claims Bühlmann Bayesian 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Year 1 Claims Bühlmann Bayesian (E) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Year 1 Claims Bühlmann Bayesian
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Exam C: Spring 2007 - 4 - GO ON TO NEXT PAGE 3. You are given: (i) Conditional on Q = q , the random variables 12 ,, , m X XX are independent and follow a Bernoulli distribution with parameter q . (ii) mm SX X X =++ + " (iii) The distribution of Q is beta with a = 1, b = 99, and θ = 1. Determine the variance of the marginal distribution of S 101 . (A) 1.00 (B) 1.99 (C) 9.09 (D) 18.18 (E) 25.25
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Exam C: Spring 2007 - 5 - GO ON TO NEXT PAGE 4. You are given the following information for a stock with current price 0.25: (i) The price of the stock is lognormally distributed with continuously compounded expected annual rate of return 0.15 α = . (ii) The dividend yield of the stock is zero. (iii) The volatility of the stock is 0.35 σ = . Using the procedure described in the McDonald text, determine the upper bound of the 90% confidence interval for the price of the stock in 6 months. (A) 0.393 (B) 0.425 (C) 0.451 (D) 0.486 (E) 0.529
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Exam C: Spring 2007 - 6 - GO ON TO NEXT PAGE 5. You are given: (i) A computer program simulates n = 1000 pseudo- U (0, 1) variates. (ii) The variates are grouped into k = 20 ranges of equal length. (iii) 20 2 1 51,850 j j O = = (iv) The Chi-square goodness-of-fit test for U (0, 1) is performed. Determine the result of the test. (A) Do not reject H 0 at the 0.10 significance level. (B) Reject H 0 at the 0.10 significance level, but not at the 0.05 significance level. (C) Reject H 0 at the 0.05 significance level, but not at the 0.025 significance level. (D) Reject H 0 at the 0.025 significance level, but not at the 0.01 significance level.
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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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edu-mc-exam-c-0507 - *BEGINNING OF EXAMINATION* 1. For a...

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