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SOA2005年11月真题ExamM北美精算师（4）

来源：高顿网校 2014-08-04

　　高顿网校小编们每天都坚持更新*7北美精算师考试的大纲：SOA2005年11月真题ExamM北美精算师（4）。
　　17. The length of time, in years, that a person will remember an actuarial statistic is modeled by

　　an exponential distribution with mean 1

　　Y . In a certain population, Y has a gamma

　　distribution with 2 α θ = = .

　　Calculate the probability that a person drawn at random from this population will remember

　　an actuarial statistic less than 1

　　2 year.

　　(A) 0.125

　　(B) 0.250

　　(C) 0.500

　　(D) 0.750

　　(E) 0.875

　　Exam M: Fall 2005 -18- GO ON TO NEXT PAGE

　　18. In a CCRC, residents start each month in one of the following three states: Independent

　　Living (State #1), Temporarily in a Health Center (State #2) or Permanently in a Health

　　Center (State #3). Transitions between states occur at the end of the month.

　　If a resident receives physical therapy, the number of sessions that the resident receives in a

　　month has a geometric distribution with a mean which depends on the state in which the

　　resident begins the month. The numbers of sessions received are independent. The number

　　in each state at the beginning of a given month, the probability of needing physical therapy in

　　the month, and the mean number of sessions received for residents receiving therapy are

　　displayed in the following table:

　　State # Number in

　　state

　　Probability of

　　needing therapy

　　Mean number

　　of visits

　　1 400 0.2 2

　　2 300 0.5 15

　　3 200 0.3 9

　　Using the normal approximation for the aggregate distribution, calculate the probability that

　　more than 3000 physical therapy sessions will be required for the given month.

　　(A) 0.21

　　(B) 0.27

　　(C) 0.34

　　(D) 0.42

　　(E) 0.50

　　Exam M: Fall 2005 -19- GO ON TO NEXT PAGE

　　19. In a given week, the number of projects that require you to work overtime has a geometric

　　distribution with 2 β= . For each project, the distribution of the number of overtime hours in

　　the week is the following:

　　x ( ) f x

　　5 0.2

　　10 0.3

　　20 0.5

　　The number of projects and number of overtime hours are independent. You will get paid for

　　overtime hours in excess of 15 hours in the week.

　　Calculate the expected number of overtime hours for which you will get paid in the week.

　　(A) 18.5

　　(B) 18.8

　　(C) 22.1

　　(D) 26.2

　　(E) 28.0

　　Exam M: Fall 2005 -20- GO ON TO NEXT PAGE

　　20. For a group of lives age x, you are given:

　　(i) Each member of the group has a constant force of mortality that is drawn from the

　　uniform distribution on [ ] 0.01, 0.02 .

　　(ii) 0.01 δ=

　　For a member selected at random from this group, calculate the actuarial present value of a

　　continuous lifetime annuity of 1 per year.

　　(A) 40.0

　　(B) 40.5

　　(C) 41.1

　　(D) 41.7

　　(E) 42.3

　　Exam M: Fall 2005 -21- GO ON TO NEXT PAGE

　　21. For a population whose mortality follows DeMoivre’s law, you are given:

　　(i) 40:40 60:60 3 e e = ?? ??

　　(ii) 20:20 60:60 e ke = ?? ??

　　Calculate k.

　　(A) 3.0

　　(B) 3.5

　　(C) 4.0

　　(D) 4.5

　　(E) 5.0

　　Exam M: Fall 2005 -22- GO ON TO NEXT PAGE

　　22. For an insurance on (x) and (y):

　　(i) Upon the first death, the survivor receives the single benefit premium for a whole life

　　insurance of 10,000 payable at the moment of death of the survivor.

　　(ii) ( ) ( ) 0.06 x y t t ? ? = = while both are alive.

　　(iii) ( ) 0.12 x y t ? =

　　(iv) After the first death, ( ) 0.10 t ? = for the survivor.

　　(v) 0.04 δ=

　　Calculate the actuarial present value of this insurance on (x) and (y).

　　(A) 4500

　　(B) 5400

　　(C) 6000

　　(D) 7100

　　(E) 7500

　　Exam M: Fall 2005 -23- GO ON TO NEXT PAGE
　　高顿网校之名人语录：青年人持久地处于一种类似陶醉的状态中，因为青春时代是甜蜜的，而且是在成长中。

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