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IOE+316+Homework+2

# IOE+316+Homework+2 - Homework#2 IOE 316 Introduction to...

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1 Homework #2 IOE 316 - Introduction to Markov Processes - Winter 2010 Homework #2 (2 pages) Answers are due before start of class on Tuesday, March 23, 2010 1. A conveyor system is used to transfer items for production to a manufacturing process. Given that the conveyor system is up (in operating state) on any day, the probability that it fails the next day is a . Given the conveyor system is down (in failed state) on any day, the probability that it is up the next day is b . What are the steady state probabilities for the system’s up and down states, expressed in terms of a and b ? 2. A taxicab driver based in Ann Arbor serves addresses in Ann Arbor, Ypsilanti, and Saline. From Ann Arbor, the driver has a probability ½ that the fare is within Ann Arbor, ¼ that the fare is to Ypsilanti, and ¼ that the fare is to Saline. From Ypsilanti, the driver has a probability ¼ that the fare is back to Ann Arbor and ¾ that the fare is to Saline.

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