hw5soln - ORIE 361 – Homework 5 August 2 2007 Answers 1(a...

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Unformatted text preview: ORIE 361 – Homework 5 August 2, 2007 Answers. 1. (a) λ = 1 1 / 2 = 2. Then F ( x ) = 1- e- 2 x . P ( X > 1 / 2) = 1- F (1 / 2) = e- 2 * 1 / 2 = e- 1 (b) By the memoryless property of exponential distribution, the probability is the same as in part (a), that is e- 1 2. Let T be the time you spend in the system,; let S i be the service time of the ith person in the queue; let R be the remaining service time of the person in service. Let S be your service time. Then we have, E [ T ] = E [ R + S 1 + S 2 + S 3 + S 4 + S ] = E [ R ] + 4 X i =1 E [ S i ] + E [ S ] S i and S are all exponential with rate μ . By the memoryless property, we conclude that R is also exponential with rate μ . E [ T ] = 1 /μ · 6 = 6 μ 3. (a) Clearly, in this case the probability is 0. (b) Let S A , S B , S C are the service times of A,B and C respectively. The only way this is possible is S A = 3, S B = 1, S C =1 . Then, probability of the event P ( S A = 3 ,S B = 1 ,S C = 1) = P ( S A = 3) P ( S B = 1) P ( S...
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hw5soln - ORIE 361 – Homework 5 August 2 2007 Answers 1(a...

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