Exercises_-_Chapters_10-11

Exercises_Chapters - ACTSCI 331 Life Contingencies I Exercises(Chapters 10-11 1 Consider a two-decrement model(1 accidental death and(2

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Exercises (Chapters 10-11) 1. Consider a two-decrement model ( (1) accidental death and (2) nonaccidental death) with (1) ( x ) = 0 : 01 , x ± 20 ; (2) ( x ) = 1 100 x , 20 ² x < 100 . Calculate (a) f T (50) ;J (15 ; 1) ; f T (50) ;J (15 ; 2) ( ) (65) ; (Answers: e & 0 : 01(15) 50 15 50 (0 : 01) , e & 0 : 01(15) 50 15 50 1 100 65 and 0 : 01 + 1 100 65 ) (b) 10 p ( ) 40 ; 10 q (2) 40 ; 10 q (1) 40 ; (Answers: e & 0 : 01(10) 60 10 60 , 1 60 1 e & 0 : 01(10) 0 : 01 and 1 ³ e & 0 : 01(10) 60 10 60 ³ 1 60 1 e & 0 : 01(10) 0 : 01 ) (c) 15 j 10 q (2) 40 and P ( J = 2) = 1 q (2) 40 ; (Answers: 1 60 e & 0 : 01(15) e & 0 : 01(25) 0 : 01 and 1 60 1 e & 0 : 01(60) 0 : 01 ) 2. We consider a three-decrement model ( (1) death, (2) withdrawal and (3) disability) with x q (1) x q (2) x q (3) x 30 0.01 0.20 0.005 31 0.01 0.20 0.004 32 0.02 0.20 0.002 . 30 years old is selected. Find (a) the expected number of survivors at age 31 and 32; (Answers: 1000 ´ 0 : 785 and 1000 ´ 0 : 785 ´ 0 : 786 ) (b) the expected number of those that will withdraw or become disabled in the next three years; (Answer: 1000 ´ f 0 : 205 + 0 : 204 ´ 0 : 785 + 0 : 202 ´ 0 : 785 ´ 0 : 786 g ) (c) the expected number of those that will die in the third year; (Answer: 1000 ´ 0 : 02 ´ 0 : 785 ´ 0 : 786 ) (d) the expected number of those that will die or become disabled in the third year. (Answer:
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This note was uploaded on 10/30/2009 for the course ACTSC 331 taught by Professor David during the Fall '09 term at Waterloo.

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Exercises_Chapters - ACTSCI 331 Life Contingencies I Exercises(Chapters 10-11 1 Consider a two-decrement model(1 accidental death and(2

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