s2004Test3

s2004Test3 - Name I.D UNIVERSITY OF WATERLOO DEPARTMENT OF...

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Unformatted text preview: Name: I.D.: UNIVERSITY OF WATERLOO DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE MID-TERM TEST #3 ACTUARIAL SCIENCE 331, SPRING 2004 EXAMINER: H.H. PANJ ER TIME: 80 minutes QUESTION AVAILABLE MARK _- 3 EXAM TOTAL 2 1. You are given the following mortality rates: AlEYYQT¥§§L§§mJ insurance policy Rays. \$1QQQ§§ the5ﬁnd,9f the of tlges'éecogd death (only if that death occurs in theijlggt .twodygggﬁ of two persons agedf89 and Premiums areaggygble for at most 2 yeél’S only while both are aliyﬂ. Assume thatr'b=0.9“.\§ Calculate: ' anw...L_,_.-M~_,~J ; _ ’ \ -- #73" 5??? ~ ll! (Tb \/ (3) b) The loss function at issue of this policy. (3) (3) . ?\ ' 3 WW u o t . c). The standard deviation of the loss function at issue. d) The loss function at time 1 if it is known that (89) died in the ﬁrst year and (8}) is still alive at time 1. L,._-_M_._m..~»wmw 5, ‘i' '3‘? x" ! - s” r .3 9;) v :- ~ "3 “A I P W! 7% 3M ~rq’.«.r". 4 (3) e) The expected value of the loss function in d) above. 31!: ﬂag if y' t ‘ ‘ *: >1 ﬁll-rte" 2. Consider two lives aged 40 and 50. You are interested in the probability that (50) dies between ages 50 and 85 after the death of (40). (3) 3.) Draw the sample space of T (40) and T(50) and indicate the region in the sample space corresponding to the event described above. I 'wa‘; "He-at -‘ g v z (3) b) Write the probability in single integral form using: (50)’s time of deat as the variable of integration. ’ ..w“ (3) c) Evaluate the integral in 0) assuming exponential future lifetime Wit mean 35 years for (50) and exp ential future lifetime with mean 42 for (40). ‘ \ I _~ zv’ w [X33 w ’J {I Ufa ‘ 1 “mi, . ‘_ - .52} :12 l; 1'“ u . r ” a 'f ~32"; .3321: K 9 ~ 3“ , 31"}? K , a '* 1. _ x , ' , {A 1" l 1: (6) 3. A life annuity is issued to four lives A,B,C, and D who are all age 27. The annuity pays 1,000 per month while all four survive, 800 per month while exactly three are alive, 600 per month While exactly two are alive and 500 while exactly one person survives. Find the net single pgemiunj for this annuity if a?) = 12.5, aﬁ? = 10, 519:2: = 8.5 and (193?” = 7. {I 5h»:- . Wr- , if“? ' i ii 3 LM. " 1 at; I) ‘ ab. r/ 3’3 .11” ’ . e :i‘ \ l 3.- \K/ E, if i f” ‘- 5170 \, i F ...
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s2004Test3 - Name I.D UNIVERSITY OF WATERLOO DEPARTMENT OF...

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