以下是北美精算师2014年考试：SOACourse6ExamC（一），请耐心看下去哦。因为高顿网校小编编写了好久才完成的，真心不容易的。
　　Exam C, Fall 2005
　　FINAL ANSWER KEY
　　Question # AnswerQuestion # Answer
　　1D 19 B
　　2A 20 A
　　3 E 21 B
　　4 B 22A
　　5 E 23E
　　6 E 24 B and C
　　7 A 25C
　　8 D 26 C
　　9 B 27A
　　10 D and E28 B
　　11D29 C
　　12 C30 D
　　13 C 31 B
　　14 C 32B
　　15A 33 E
　　16 D 34A
　　17 D 35 E
　　18A
 
　　Exam C: Fall 2005 -1- GO ON TO NEXT PAGE
　　**BEGINNING OF EXAMINATION**
　　1. A portfolio of policies has produced the following claims:
　　100 100 100 200 300 300 300 400 500 600
　　Determine the empirical estimate of H(300).
　　(A) Less than 0.50
　　(B) At least 0.50, but less than 0.75
　　(C) At least 0.75, but less than 1.00
　　(D) At least 1.00, but less than 1.25
　　(E) At least 1.25
 
　　Exam C: Fall 2005 -2- GO ON TO NEXT PAGE
　　2. You are given:
　　(i) The conditional distribution of the number of claims per policyholder is Poisson with
　　mean λ .
　　(ii) The variable λ has a gamma distribution with parameters α and θ .
　　(iii) For policyholders with 1 claim in Year 1, the credibility estimate for the number of
　　claims in Year 2 is 0.15.
　　(iv) For policyholders with an average of 2 claims per year in Year 1 and Year 2, the
　　credibility estimate for the number of claims in Year 3 is 0.20.
　　Determine θ .
　　(A) Less than 0.02
　　(B) At least 0.02, but less than 0.03
　　(C) At least 0.03, but less than 0.04
　　(D) At least 0.04, but less than 0.05
　　(E) At least 0.05
 
　　Exam C: Fall 2005 -3- GO ON TO NEXT PAGE
　　3. A random sample of claims has been drawn from a Burr distribution with known parameter
　　α = 1 and unknown parameters θ and γ . You are given:
　　(i) 75% of the claim amounts in the sample exceed 100.
　　(ii) 25% of the claim amounts in the sample exceed 500.
　　Estimate θ by percentile matching.
　　(A) Less than 190
　　(B) At least 190, but less than 200
　　(C) At least 200, but less than 210
　　(D) At least 210, but less than 220
　　(E) At least 220
 
　　Exam C: Fall 2005 -4- GO ON TO NEXT PAGE
　　4. You are given:
　　(i) f ( x) is a cubic spline with knots (0, 0) and (2, 2).
　　(ii) f ′(0) = 1 and f ′′(2) = ?24
　　Determine f (1).
　　(A) 1
　　(B) 4
　　(C) 6
　　(D) 8
　　(E) 10
 
　　Exam C: Fall 2005 -5- GO ON TO NEXT PAGE
　　5. For a portfolio of policies, you are given:
　　(i) There is no deductible and the policy limit varies by policy.
　　(ii) A sample of ten claims is:
　　350 350 500 500 500+ 1000 1000+ 1000+ 1200 1500
　　where the symbol + indicates that the loss exceeds the policy limit.
　　(iii) ^
　　S1(1250) is the product-limit estimate of S(1250).
　　(iv) ^
　　S2 (1250) is the maximum likelihood estimate of S(1250) under the assumption that
　　the losses follow an exponential distribution.
　　Determine the absolute difference between ^
　　S1(1250) and ^
　　S2 (1250) .
　　(A) 0.00
　　(B) 0.03
　　(C) 0.05
　　(D) 0.07
　　(E) 0.09
　　Exam C: Fall 2005 -6- GO ON TO NEXT PAGE
　　高顿网校之名人哲理：衣服和风度并不能造就一个人；但对一个已经造就的人，它们可以大大增进他的仪表。所谓男子气概是指亲切、慈爱的风度，而不是指肉体上的意愿而言。——萨迪