SOA真题Course6ExamC(1)

1、姓名：_ 班级：_ 学号：_-密-封 -线- soa真题course6examc(1)考试时间：120分钟 考试总分：100分题号一二三四五总分分数遵守考场纪律，维护知识尊严，杜绝违纪行为，确保考试结果公正。question # answerquestion # answer1d 19 b2a 20 a3 e 21 b4 b 22a5 e 23e6 e 24 b and c7 a 25c8 d 26 c9 b 27a10 d and e28 b11d29 c12 c30 d13 c 31 b14 c 32b15a 33 e16 d 34a17 d 35 e18aexam c: fall 200

2、5 -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 600determine 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.

3、00, but less than 1.25(e) at least 1.25exam c: fall 2005 -2- go on to next page2. you are given:(i) the conditional distribution of the number of claims per policyholder is poisson withmean .(ii) the variable has a gamma distribution with parameters and .(iii) for policyholders with 1 claim in year

4、1, the credibility estimate for the number ofclaims in year 2 is 0.15.(iv) for policyholders with an average of 2 claims per year in year 1 and year 2, thecredibility estimate for the number of claims in year 3 is 0.20.determine .(a) less than 0.02(b) at least 0.02, but less than 0.03(c) at least 0.

5、03, but less than 0.04(d) at least 0.04, but less than 0.05(e) at least 0.05exam c: fall 2005 -3- go on to next page3. a random sample of claims has been drawn from a burr distribution with known parameter = 1 and unknown parameters and . you are given:(i) 75% of the claim amounts in the sample exce

6、ed 100.(ii) 25% of the claim amounts in the sample exceed 500.estimate by percentile matching.(a) less than 190(b) at least 190, but less than 200(c) at least 200, but less than 210l(c) 6(d) 8(e) 10exam c: fall 2005 -5- go on to next page5. for a portfolio of policies, you are given:(i) there is no

7、deductible and the policy limit varies by policy.(ii) a sample of ten claims is:350 350 500 500 500+ 1000 1000+ 1000+ 1200 1500where the symbol + indicates that the loss exceeds the policy limit.(iii) ls1(1250) is the product-limit estimate of s(1250).(iv) ls2 (1250) is the maximum likelihood estima

8、te of s(1250) under the assumption thatthe losses follow an exponential distribution.determine the absolute difference between ls1(1250) and ls2 (1250) .(a) 0.00(b) 0.03(c) 0.05(d) 0.08(e) 0.09exam c: fall 2005 -6- go on to next page determine the bhlmann-straub empirical bayes estimate of the credi

9、bility factor z forterritory 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 0.7exam c: fall 2005 -23- go on to next page23. determine which of the following is a natural cubic spline passing through the threepo

10、ints (0, y1 ), (1, y2 ), and (3, 6).(a) ( )( )( )( ) ( )( ) ( )( )32 33 7/6 , 0 12 1/6 1 11/6 1 11/24 1 , 1 3x x xf xx x x x= + + (b) ( )( ) ( )( )2 32 33 , 0 12 2 1 1/2 1 , 1 3x x x xf xx x x= + + (c) ( )( ) ( )( )( ) ( ) ( )( )2 32 33 1/2 1/2 , 0 12 1/2 1 1 1/8 1 , 1 3x x x xf xx x x x= + + (d) (

11、)( ) ( ) ( )( )( ) ( )( )2 32 33 5/ 4 1/2 3/ 4 , 0 12 7/4 1 3/8 1 , 1 3x x x xf xx x x= + + (e) ( )( ) ( )( )( ) ( )( )32 33 3/2 1/2 , 0 12 3/ 2 1 1/ 4 1 , 1 3x x xf xx x x= + + exam c: fall 2005 -24- go on to next page24. you are given:(i) a cox proportional hazards model was used to study the surv

12、ival times ofpatients 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 femalepatient.(iii) a sample of five patients gave the following survival times (in months):males: 10 18 25females: 15 21(iv) the parameter es

13、timate is = 0.27.using the nelson-aalen estimate of the baseline cumulative hazard function, estimate the,财会考试.精算师考试, probability that a future female patient will survive more than 20 months from the time ofthe onset of the disease.(a) 0.33(b) 0.36(c) 0.40(d) 0.43(e) 0.50exam c: fall 2005 -25- go o

14、n to next page(c) 0.06(d) 0.09(e) 0.12exam c: fall 2005 -30- go on to next page30. for a group of auto policyholders, you are given:(i) the number of claims for each policyholder has a conditional poissondistribution.(ii) during year 1, the following data are observed for 8000 policyholders:number o

15、f claims number of policyholders0 50001 21002 7503 1004 505+ 0a randomly selected policyholder had one claim in year 1.determine the semiparametric empirical bayes estimate of the number of claims inyear 2 for the same policyholder.(a) less than 0.15(b) at least 0.15, but less than 0.30(c) at least

16、0.30, but less than 0.45(d) at least 0.45, but less than 0.60(e) at least 0.60exam c: fall 2005 -31- go on to next page31. you are given:(i) the following are observed claim amounts:400 1000 1600 3000 5000 5400 6200(ii) an exponential distribution with = 3300 is hypothesized for the data.(iii) the go