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# Quiz_4 - that server is free or else remains with server...

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21 April 2009 IE 304 OPERATIONS RESEARCH III: STOCHASTIC MODELS QUIZ # 4 Duration: 40 mins Question 1) The time T required to repair a machine is an exponentially distributed random variable with mean ½ hours. (a) What is the probability that a repair time exceeds ½ hours? (b) What is the probability that a repair takes at least 12 ½ hours given that its duration exceeds 12 hours? Question 2) In a certain system, a customer must first be served by server 1 and then by server 2. The service times at server i are exponential with rate μ i , i = 1, 2 . An arrival finding server 1 busy waits in line for that server. Upon completion of service at server 1, a customer either enters service with server 2 if
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Unformatted text preview: that server is free or else remains with server 1 (blocking any other customer from entering service) until server 2 is free. Customers depart the system after being served by server 2. Suppose that when you arrive there is one customer in the system and that customer is being served by server 1. What is the expected total time you spend in the system? Question 3) Let X 1 and X 2 be independent exponential random variables. Without any computations, tell which one of the followings is correct. Explain your answer. (a) E[X 1 +X 2 | X 1 > 1] = E[X 2 + 1] (b) E[X 1 +X 2 | X 1 > 1] = E[X 1 +X 2 ] + 1 (c) E[X 1 +X 2 | X 1 > 1] = E[X 1 ] + E[X 2 ]...
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