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北美精算师考试SOA——历年真题Course6ExamC（最后一部分）

来源：高顿网校 2014-07-22

　　以下则是北美精算师考试SOA——历年真题Course6ExamC（最后一部分），珍惜小编的辛勤劳作。
　　32. You are given:

　　(i) In a portfolio of risks, each policyholder can have at most two claims per year.

　　(ii) For each year, the distribution of the number of claims is:

　　Number of Claims Probability

　　0 0.10

　　1 0.90? q

　　2 q

　　(iii) The prior density is:

　　2

　　( ) , 0.2 0.5

　　0.039

　　πq= q <q<

　　A randomly selected policyholder had two claims in Year 1 and two claims in Year 2.

　　For this insured, determine the Bayesian estimate of the expected number of claims in

　　Year 3.

　　(A) Less than 1.30

　　(B) At least 1.30, but less than 1.40

　　(C) At least 1.40, but less than 1.50

　　(D) At least 1.50, but less than 1.60

　　(E) At least 1.60

　　Exam C: Fall 2005 -33- GO ON TO NEXT PAGE

　　33. For 500 claims, you are given the following distribution:

　　Claim Size Number of Claims

　　[0, 500) 200

　　[500, 1,000) 110

　　[1,000, 2,000) x

　　[2,000, 5,000) y

　　[5,000, 10,000) ?

　　[10,000, 25,000) ?

　　[25,000, ∞) ?

　　You are also given the following values taken from the ogive:

　　F

　　500(1500) = 0.689

　　F

　　500(3500) = 0.839

　　Determine y.

　　(A) Less than 65

　　(B) At least 65, but less than 70

　　(C) At least 70, but less than 75

　　(D) At least 75, but less than 80

　　(E) At least 80

　　Exam C: Fall 2005 -34- GO ON TO NEXT PAGE

　　34. Which of statements (A), (B), (C), and (D) is false?

　　(A) The chi-square goodness-of-fit test works best when the expected number of

　　observations varies widely from interval to interval.

　　(B) For the Kolmogorov-Smirnov test, when the parameters of the distribution in the

　　null hypothesis are estimated from the data, the probability of rejecting the null

　　hypothesis decreases.

　　(C) For the Kolmogorov-Smirnov test, the critical value for right censored data should

　　be smaller than the critical value for uncensored data.

　　(D) The Anderson-Darling test does not work for grouped data.

　　(E) None of (A), (B), (C) or (D) is false.

　　Exam C: Fall 2005 -35- STOP

　　35. You are given:

　　(i) The number of claims follows a Poisson distribution.

　　(ii) Claim sizes follow a gamma distribution with parameters α (unknown) and

　　θ = 10,000 .

　　(iii) The number of claims and claim sizes are independent.

　　(iv) The full credibility standard has been selected so that actual aggregate losses will

　　be within 10% of expected aggregate losses 95% of the time.

　　Using limited fluctuation (classical) credibility, determine the expected number of claims

　　required for full credibility.

　　(A) Less than 400

　　(B) At least 400, but less than 450

　　(C) At least 450, but less than 500

　　(D) At least 500

　　(E) The expected number of claims required for full credibility cannot be determined

　　from the information given.

　　**END OF EXAMINATION**
　　高顿网校之名人名言：没有一种绰约动人、真实可感的风度之美，可以不借助自然之美的营养。——金马

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