SOA往年考试真题北美精算师的Course6ExamC（4），请先背诵完，然后慢慢累积所有北美精算师的知识点。
　　19. For a portfolio of independent risks, the number of claims for each risk in a year follows
　　a Poisson distribution with means given in the following table:
　　Class
　　Mean Number of
　　Claims per Risk Number of Risks
　　1 1 900
　　2 10 90
　　3 20 10
　　You observe x claims in Year 1 for a randomly selected risk.
　　The Bühlmann credibility estimate of the number of claims for the same risk in Year 2 is
　　11.983.
　　Determine x.
　　(A) 13
　　(B) 14
　　(C) 15
　　(D) 16
　　(E) 17
　　Exam C: Fall 2005 -20- GO ON TO NEXT PAGE
　　20. A survival study gave (0.283, 1.267) as the symmetric linear 95% confidence interval
　　for H(5).
　　Using the delta method, determine the symmetric linear 95% confidence interval for S(5).
　　(A) (0.23, 0.69)
　　(B) (0.26, 0.72)
　　(C) (0.28, 0.75)
　　(D) (0.31, 0.73)
　　(E) (0.32, 0.80)
　　Exam C: Fall 2005 -21- GO ON TO NEXT PAGE
　　21. You are given:
　　(i) Losses on a certain warranty product in Year i follow a lognormal distribution
　　with parameters i
　　μ and i
　　σ .
　　(ii) i
　　σ =σ , for i = 1, 2, 3,…
　　(iii) The parameters i
　　μ vary in such a way that there is an annual inflation rate of 10%
　　for losses.
　　(iv) The following is a sample of seven losses:
　　Year 1: 20 40 50
　　Year 2: 30 40 90 120
　　Using trended losses, determine the method of moments estimate of μ3 .
　　(A) 3.87
　　(B) 4.00
　　(C) 30.00
　　(D) 55.71
　　(E) 63.01
　　Exam C: Fall 2005 -22- GO ON TO NEXT PAGE
　　22. You are given:
　　(i) A region is comprised of three territories. Claims experience for Year 1 is as
　　follows:
　　Territory Number of Insureds Number of Claims
　　A 10 4
　　B 20 5
　　C 30 3
　　(ii) The number of claims for each insured each year has a Poisson distribution.
　　(iii) Each insured in a territory has the same expected claim frequency.
　　(iv) The number of insureds is constant over time for each territory.
　　Determine the Bühlmann-Straub empirical Bayes estimate of the credibility factor Z for
　　Territory A.
　　(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
　　Exam C: Fall 2005 -23- GO ON TO NEXT PAGE
　　23. Determine which of the following is a natural cubic spline passing through the three
　　points (0, y1 ), (1, y2 ), and (3, 6).
　　(A) ( )
　　( )
　　( )( ) ( )( ) ( )( )
　　3
　　2 3
　　3 7/6 , 0 1
　　2 1/6 1 11/6 1 11/24 1 , 1 3
　　x x x
　　f x
　　x x x x
　　= ≤
　　+ + ≤ ≤
　　(B) ( )
　　( ) ( )( )
　　2 3
　　2 3
　　3 , 0 1
　　2 2 1 1/2 1 , 1 3
　　x x x x
　　f x
　　x x x
　　= + ≤
　　+ ≤ ≤
　　(C) ( )
　　( ) ( )
　　( )( ) ( ) ( )( )
　　2 3
　　2 3
　　3 1/2 1/2 , 0 1
　　2 1/2 1 1 1/8 1 , 1 3
　　x x x x
　　f x
　　x x x x
　　= + ≤
　　+ ≤ ≤
　　(D) ( )
　　( ) ( ) ( )
　　( )( ) ( )( )
　　2 3
　　2 3
　　3 5/ 4 1/2 3/ 4 , 0 1
　　2 7/4 1 3/8 1 , 1 3
　　x x x x
　　f x
　　x x x
　　= + ≤
　　+ ≤ ≤
　　(E) ( )
　　( ) ( )
　　( )( ) ( )( )
　　3
　　2 3
　　3 3/2 1/2 , 0 1
　　2 3/ 2 1 1/ 4 1 , 1 3
　　x x x
　　f x
　　x x x
　　= + ≤
　　+ ≤ ≤
　　Exam C: Fall 2005 -24- GO ON TO NEXT PAGE
　　24. You are given:
　　(i) A Cox proportional hazards model was used to study the survival times of
　　patients with a certain disease from the time of onset to death.
　　(ii) A single covariate z was used with z = 0 for a male patient and z = 1 for a female
　　patient.
　　(iii) A sample of five patients gave the following survival times (in months):
　　Males: 10 18 25
　　Females: 15 21
　　(iv) The parameter estimate is β= 0.27.
　　Using the Nelson-Aalen estimate of the baseline cumulative hazard function, estimate the
　　probability that a future female patient will survive more than 20 months from the time of
　　the onset of the disease.
　　(A) 0.33
　　(B) 0.36
　　(C) 0.40
　　(D) 0.43
　　(E) 0.50
　　Exam C: Fall 2005 -25- GO ON TO NEXT PAGE
　　高顿网校之短句汇编：只有在颠沛流离之后，才能重新应证时间在内心留下的痕迹。