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# ex-5 - Spring 2011 OR3510/5510 Problem Set 5 Reading You...

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Spring 2011 OR3510/5510 Problem Set 5 Reading: You should be browsing in Chapter 5 after memorizing Chapter 4. Because of the upcoming prelim, do not hand this in. However, you are responsible for the material. 1. The lifetime of a radio is exponentially distributed with a mean of ten years. If Jones buys a ten-year-old radio, what is the probability that it will be working after an additional ten years? 2. The time T required to repair a machine is an exponentially distributed ran- dom variable with mean 1/2 hour. (a) What is the probability that a repair time exceeds 1/2 hour? (b) What is the probability that a repair takes at least 12 1/2 hours given that its duration exceeds 12 hours? 3. A post office has two clerks. Three people, Ann, Bruce, and Charles, enter simultaneously. Ann and Bruce go directly to the clerks, and Charles waits until either Ann or Bruce leaves before he begins service. What is the probability that Ann is still in the post office after the other two have left when (a) the service time for each clerk is exactly (nonrandom) ten minutes?
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