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Unformatted text preview: m wax Name:
I.D.: UNIVERSITY OF WATERLOO
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
MIDTERM TEST #4 ACTUARIAL SCIENCE 331, SPRING 2004 EXAMINER: H.H. PANJER TIME: 80 minutes QUESTION AVAILABLE MARK » $1" 1. A multiple decrement table with 2 causes of death has the joint p.d.f. 0.03+0.002t, 0<t$10, j=1
f(t,j)= 0.04+0.004t, O<t$10, j=2 0, otherwise
Find: (a) The marginal distribution of the time to death.
(b) The marginal distribution of the cause of death. (c) The distribution of the time to death if it is known that J = 1. (d) The probability that J = 1, if it is know that T = 5. 3
2. A triple—decrement service table has the following entries at age 3::
1
g) = 0.06
9 = 0.12
9) = 0.03
Where (1) refers to death, (2) refers to disability and (3) refers to re
tirement. a , ( 3
Em
Find the probabilities of death, disability and retirement in the as
sociated single decrement tables. Assume that each decrement has a
constant force over the one—year interval (as, x + 1] CW.“ {wit ! new ,jﬂ‘fy :: {if} “vi"‘3’
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l  g 1 .l 3. You are given the following information for a person age :13: i) The probability of death in the next year in the associated sin gle decrement mortality table is 0.20. Deaths are uniformly dis— tributed , oughout the year. 1 ‘ ii) Ignoring death (i.e. in the associated single decrement table) the A ,9. 4., r; W probability of retirement in the next year is 0.30. Half of retire
merits occur wayxthrough the year. The remainder occur at
‘ 73.?” .  ’7? 7 ‘~.
2" ’ year end: Find: (a) The probability that the person remains active at age :1: + 1. (b) The probability that the person dies while in service before age
a: + 1 (c) The probability that the person retires before or at age as + 1. iii; 1 4. A Whole life insurance policy issued to (x) pays $1000 only on accidental death. Assume: «‘g. i) a force of accidental death of .005 for all ages. ' <1 "“ " ""
ii) a force of nonaccidental death of .015 for all ages. ; 2 ;; iii) a force of interest of .050. :: gm ‘17 (a) Find the net annual (fully continuous) premium for this policy. (b) If death occurs at age a: + t, what is the probability that it was accidental? (c) If is alive in 10 years, What is the reserve at age a: + 10? PM i
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 Spring '09
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