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Unformatted text preview: IEOR 161 Operations Research II University of California, Berkeley Spring 2008 Homework 6 Suggested Solution Chapter 5. 58. Let X j be the time it takes for the first type j coupon collected. P { i is the last type collected } = P { X i = max j =1 ,...,n X j } = Z ( X j < x j 6 = i ) i e i x dx = Z Y j 6 = i (1 e j x ) i e i x dx = Z 1 Y j 6 = i (1 y j / i ) dy ( y = e i x ) = E " Y j 6 = i (1 U j / i ) # 68. (a) E [ A ( t )  N ( t ) = n ] = E " n X i =1 A i e ( t S i ) # = E [ A ] e t E " n X i =1 e U [ i ] # = E [ A ] e t E " n X i =1 e U i # = nE [ A ] e t E e U = nE [ A ] e t Z t e x 1 t dx = nE [ A ] 1 e t t E [ A ( t )] = E [ E [ A ( t )  N ( t ) = n ]] = E [ N ( t )] E [ A ] 1 e t t = E [ A ] 1 e t t t = E [ A ] (1 e t ) (b) Going backwards from time t to 0, events occur according to a Poisson process and an event occurring at time s has value Ae s attached to it....
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This note was uploaded on 03/03/2009 for the course IEOR 161 taught by Professor Lim during the Fall '08 term at University of California, Berkeley.
 Fall '08
 Lim
 Operations Research

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