Chapter_8a_-_Question_Set

Chapter_8a_-_Question_Set - ACTSCI 331 Life Contingencies I...

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Unformatted text preview: ACTSCI 331 - Life Contingencies I Exercises (Chapter 8a) 1. Let T ( x ) and T ( y ) be two independent rv&s. Given that 20 p x = 0 : 9 and 20 p y = 0 : 8 , ¡nd 20 p xy and 20 p xy . (Answers : : 72 and : 98 ) 2. Let the joint p.d.f. of ( T ( x ) ;T ( y )) be given by f T ( x ) ;T ( y ) ( t;s ) = 1 4 & 2 e & & ( t + s ) + 3 4 ¡ 2 e & ¡ ( t + s ) ; t;s > ; with & = 0 : 01 and ¡ = 0 : 02 . Calculate Pr(20 < T ( xy ) < 50) and Pr(20 < T ( xy ) < 50) . (Answers: : 311 and : 249 ). 3. Suppose & 10 p x = 0 : 9 and 30 p x = 0 : 5 & 10 q y = 0 : 15 and 30 q y = 0 : 45 Under the independent assumption, ¡nd (a) Pr (the ¡rst death amongst ( x ) and ( y ) occurs between times 10 and 30 ). (Answer: : 49 ) (b) Pr (at most one death amongst ( x ) and ( y ) occurs between times 10 and 30 ). (Answer: : 88 ) (c) Pr (the second death amongst ( x ) and ( y ) occurs between times 10 and 30 ). (Answer: : 21 ) 4. Prove that for two events, say A and B , max( P ( A ) + P ( B ) ¡ 1 ; 0) ¢ P ( A and B ) ¢ min( P ( A ) ;P ( B )) . (1) From (1), ¡nd a two-sided inequality for t p xy ....
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Chapter_8a_-_Question_Set - ACTSCI 331 Life Contingencies I...

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