# 416-8 - a E X 2 | X> 1 = E X 1 2 b E X 2 | X> 1 = E X 2...

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Denker Spring 2010 416 Stochastic Modeling - Assignment 8 Due Date: Monday, March 22, 2010 Problem 1: (Problem 1, p. 346) The time required to repair a machine is an expoenentially distributed random variable with mean 0.5 hours. What is the probability that the repair takes at least 12.5 hours given that its duration exceeds 12 hours? Problem 2: (Problem 2, p. 346) Suppose you arrive at a single-teller bank to find five other customers in the bank, one being served, the other four waiting in line. You join the end of the line. If the service times are all exponential with rate μ , what is the expected time you will spend in the bank? Problem 3: (Problem 3, p. 346) Let X be an exponential random variable. Which of the following formulas are correct?
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Unformatted text preview: a) E [ X 2 | X > 1] = E [( X + 1) 2 ], b) E [ X 2 | X > 1] = E [ X 2 ] + 1, c) E [ X 2 | X > 1] = (1 + E [ X ]) 2 ? Problem 4: (Problem 5, p. 346) The liFetime oF a radio is exponentially distributed with mean oF ten years. IF you buy a ten year old radio what is the probability that it will be working For another ten years? Problem 5: (Problem 9, p. 347) Machine 1 is currently working. Machine 2 will be put into use at a time t From now. IF the liFetime oF the machine i is exponential with rate λ i , i = 1 , 2, what is the probability that machine 1 is the frst machine to Fail?...
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