# Exam C_1106 - Preliminary Exam C Fall 2006 ANSWER KEY...

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Preliminary Exam C, Fall 2006 ANSWER KEY Question # Answer Question # Answer 1 E 19 B 2 D 20 D 3 B 21 A 4 C 22 A 5 A 23 E 6 D 24 E 7 B 25 D 8 C 26 A 9 E 27 C 10 D 28 C 11 E 29 C 12 B 30 B 13 C 31 C 14 A 32 A 15 B 33 B 16 E 34 A 17 D 35 A 18 D

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Exam C: Fall 2006 - 1 - GO ON TO NEXT PAGE **BEGINNING OF EXAMINATION** 1. You are given: (i) Losses follow a Burr distribution with α = 2. (ii) A random sample of 15 losses is: 195 255 270 280 350 360 365 380 415 450 490 550 575 590 615 (iii) The parameters γ and θ are estimated by percentile matching using the smoothed empirical estimates of the 30 th and 65 th percentiles. Calculate the estimate of . (A) Less than 2.9 (B) At least 2.9, but less than 3.2 (C) At least 3.2, but less than 3.5 (D) At least 3.5, but less than 3.8 (E) At least 3.8
Exam C: Fall 2006 - 2 - GO ON TO NEXT PAGE 2. An insurance company sells three types of policies with the following characteristics: Type of Policy Proportion of Total Policies Annual Claim Frequency I 5% Poisson with 0.25 λ = II 20% Poisson with 0.50 = III 75% Poisson with 1.00 = A randomly selected policyholder is observed to have a total of one claim for Year 1 through Year 4. For the same policyholder, determine the Bayesian estimate of the expected number of claims in Year 5. (A) Less than 0.4 (B) At least 0.4, but less than 0.5 (C) At least 0.5, but less than 0.6 (D) At least 0.6, but less than 0.7 (E) At least 0.7

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Exam C: Fall 2006 - 3 - GO ON TO NEXT PAGE 3. You are given a random sample of 10 claims consisting of two claims of 400, seven claims of 800, and one claim of 1600. Determine the empirical skewness coefficient. (A) Less than 1.0 (B) At least 1.0, but less than 1.5 (C) At least 1.5, but less than 2.0 (D) At least 2.0, but less than 2.5 (E) At least 2.5
Exam C: Fall 2006 - 4 - GO ON TO NEXT PAGE 4. You are given: (i) The cumulative distribution for the annual number of losses for a policyholder is: n ( ) N F n 0 0.125 1 0.312 2 0.500 3 0.656 4 0.773 5 0.855 M M (ii) The loss amounts follow the Weibull distribution with θ = 200 and τ = 2. (iii) There is a deductible of 150 for each claim subject to an annual maximum out-of- pocket of 500 per policy. The inversion method is used to simulate the number of losses and loss amounts for a policyholder. (a) For the number of losses use the random number 0.7654. (b) For loss amounts use the random numbers: 0.2738 0.5152 0.7537 0.6481 0.3153 Use the random numbers in order and only as needed. Based on the simulation, calculate the insurer’s aggregate payments for this policyholder. (A) 106.93 (B) 161.32 (C) 224.44 (D) 347.53 (E) 520.05

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Exam C: Fall 2006 - 5 - GO ON TO NEXT PAGE 5. You have observed the following three loss amounts: 186 91 66 Seven other amounts are known to be less than or equal to 60. Losses follow an inverse exponential with distribution function () / ,0 x Fx e x θ = > Calculate the maximum likelihood estimate of the population mode. (A) Less than 11 (B) At least 11, but less than 16 (C) At least 16, but less than 21 (D) At least 21, but less than 26 (E) At least 26
Exam C: Fall 2006 - 6 - GO ON TO NEXT PAGE 6.

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Exam C_1106 - Preliminary Exam C Fall 2006 ANSWER KEY...

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