有正在学习此页的精算师学生咩？SOA精算师考试——真题精选November2005ExamM（四），请多看看啦。
　　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
　　高顿网校之名人哲学：每个人都应该担负起应尽的责任。——徐磊刚