November2005ExamM真题系列（Part2）——北美精算师考试SOA，高顿网校小编友善热情提醒小伙伴们拿出恒心，与考试抗战到底。
　　5. A certain species of flower has three states: sustainable, endangered and extinct. Transitions
　　between states are modeled as a non-homogeneous Markov chain with transition matrices i Q
　　as follows:
　　1
　　Endangered Sustainable Extinct
　　Sustainable 0.85 0.15 0
　　0 0.7 0.3 Endangered
　　Extinct 0 0 1
　　Q
　　=
　　2
　　0.9 0.1 0
　　0.1 0.7 0.2
　　0 0 1
　　Q
　　=
　　3
　　0.95 0.05 0
　　0.2 0.7 0.1
　　0 0 1
　　Q
　　=
　　0.95 0.05 0
　　0.5 0.5 0 , 4,5,...
　　0 0 1
　　iQ i
　　= =
　　Calculate the probability that a species endangered at the start of year 1 will ever become
　　extinct.
　　(A) 0.45
　　(B) 0.47
　　(C) 0.49
　　(D) 0.51
　　(E) 0.53
　　Exam M: Fall 2005 -6- GO ON TO NEXT PAGE
　　6. For a special 3-year term insurance:
　　(i) Insureds may be in one of three states at the beginning of each year: active, disabled,
　　or dead. All insureds are initially active. The annual transition probabilities are as
　　follows:
　　Active Disabled Dead
　　Active 0.8 0.1 0.1
　　Disabled 0.1 0.7 0.2
　　Dead 0.0 0.0 1.0
　　(ii) A 100,000 benefit is payable at the end of the year of death whether the insured was
　　active or disabled.
　　(iii) Premiums are paid at the beginning of each year when active. Insureds do not pay
　　any annual premiums when they are disabled.
　　(iv) d = 0.10
　　Calculate the level annual benefit premium for this insurance.
　　(A) 9,000
　　(B) 10,700
　　(C) 11,800
　　(D) 13,200
　　(E) 20,800
　　Exam M: Fall 2005 -7- GO ON TO NEXT PAGE
　　7. Customers arrive at a bank according to a Poisson process at the rate of 100 per hour. 20%
　　of them make only a deposit, 30% make only a withdrawal and the remaining 50% are there
　　only to complain. Deposit amounts are distributed with mean 8000 and standard deviation
　　1000. Withdrawal amounts have mean 5000 and standard deviation 2000.
　　The number of customers and their activities are mutually independent.
　　Using the normal approximation, calculate the probability that for an 8-hour day the total
　　withdrawals of the bank will exceed the total deposits.
　　(A) 0.27
　　(B) 0.30
　　(C) 0.33
　　(D) 0.36
　　(E) 0.39
　　Exam M: Fall 2005 -8- GO ON TO NEXT PAGE
　　8. A Mars probe has two batteries. Once a battery is activated, its future lifetime is exponential
　　with mean 1 year.
　　The first battery is activated when the probe lands on Mars. The second battery is activated
　　when the first fails.
　　Battery lifetimes after activation are independent.
　　The probe transmits data until both batteries have failed.
　　Calculate the probability that the probe is transmitting data three years after landing.
　　(A) 0.05
　　(B) 0.10
　　(C) 0.15
　　(D) 0.20
　　(E) 0.25
　　Exam M: Fall 2005 -9- GO ON TO NEXT PAGE
　　高顿网校之谚语相赠：青年的形象应该是纯洁、热情、有正确批评能力的。