Exercises_-_Chapter_9

# Exercises_-_Chapter_9 - ACTSCI 331 - Life Contingencies I...

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Unformatted text preview: ACTSCI 331 - Life Contingencies I Exercises (Chapter 9) 1. Let T ( x ) and T ( y ) be two independent random variables. Given that 20 p x = 0 : 9 and 20 p y = 0 : 8 , &nd 20 p xy and 20 p xy . (Answers : 0.72 and 0.98). 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 & = : 01 and ¡ = : 02 . Calculate Pr ( 20 <T ( xy ) < 50 ) and Pr ( 20 <T ( xy ) < 50 ). (Answers: 0.311 and 0.249). 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: 0.49); (b) Pr (at most one death amongst ( x ) and ( y ) occurs between times 10 and 30). (Answer: 0.88); (c) Pr (the second death amongst ( x ) and ( y ) occurs between times 10 and 30). (Answer: 0.21); 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...
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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_-_Chapter_9 - ACTSCI 331 - Life Contingencies I...

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