hw6sln - IEOR 161 Operations Research II University of...

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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.

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hw6sln - IEOR 161 Operations Research II University of...

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