ISyE 3232CStochastic Manufacturing and Service SystemsSpring 2010Practice Test 3Closed book, closed notes, no electronics.1. Arriving at a beauty salon, Sue finds Liz and Grace being served by two beauticians. Sue will be servedas soon as Liz or Grace leaves. Liz is having a perm, and Grace a manicure. The duration of a permis exponentially distributed with rate 2/hr and the duration of a manicure is exponentially distributedwith rate 3/hr. Assuming that Sue needs a perm.(a) What is the expected time that Sue spends in the beauty salon?(b) What is the probability that Sue leaves last?(c) What is the probability that Liz leaves last?2. Two individuals, A and B, both require kidney transplants. If she does not receive a new kidney, thenA will die after an exponential amount of time with parameterμA, and B after an exponential amountof time with parameterμB.New kidneys arrive according to a Poisson process with rateλ.It has
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Probability theory, Exponential distribution, Poisson process, Sue, Liz