s2004Test4 - m wax- Name: I.D.: UNIVERSITY OF WATERLOO...

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Unformatted text preview: m wax- Name: I.D.: UNIVERSITY OF WATERLOO DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE MID-TERM 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’ . J; l . 51 j ’ '- J. a {W 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 ‘ 7-3.?” . - ’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 non-accidental 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 l a 5 , a M {r} ‘5 g g” UHKW , A" a is: . 2t ~- '4: M” H ‘ 4 ' 0‘0 4:4,;- 3 5’ [MN 1? r M 1 ' , / F "in p 12‘ I 1“? l l - ? i u . J 40‘ m r "J 43"]. l "’0'; 5 f I “0‘1,” g,» u .. uni—Mr ' _..-— i( 0“ J a l (I W \ - b.1337 :1 0 0‘; J ) ’3 9 E 9W” ( 9) u"? L 7 a "m? [L )I} ‘ \~ 1., ’ a w ~ w w 4 ~ ., "w . on 4 ,1 Db, V Anal ‘ rqlfi , V, .a a V , _.- - DA 1:1,}: ‘“ jai L: 4 4* a e, a « I .u 90-} 1 £3 0 u? ...
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s2004Test4 - m wax- Name: I.D.: UNIVERSITY OF WATERLOO...

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