Practice Test 3

Practice Test 3 - ISyE 3232C Stochastic Manufacturing and...

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Unformatted text preview: ISyE 3232C Stochastic Manufacturing and Service Systems Spring 2010 Practice Test 3 Closed book, closed notes, no electronics. 1. Arriving at a beauty salon, Sue finds Liz and Grace being served by two beauticians. Sue will be served as soon as Liz or Grace leaves. Liz is having a perm, and Grace a manicure. The duration of a perm is exponentially distributed with rate 2/hr and the duration of a manicure is exponentially distributed with 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, then A will die after an exponential amount of time with parameter A , and B after an exponential amount of time with parameter B . New kidneys arrive according to a Poisson process with rate . It has been decided that the first kidney will go to A (or to B if B is alive and A is not at the time), and the...
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