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# ex_1 - will begin the process by entering step 1 After step...

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Spring 2009 OR3510/5510 Problem Set 1 Due Monday Feb 2 at 10am in the homework box between Rhodes and Upson. Reading: You should have reviewed Chapters 1-3, and be browsing in Chapter 4. x/y=page x, problem y in Ross. 1. 94/62 2. 171/33 3. 264/5 4. 264/8 5. A taxi driver moves from airport A and two hotels B and C according to the following rules. If he is at the airport, he will be at one of the two hotels next with equal probability. If at a hotel, then he returns to the airport with probability 3/4 and goes to the other hotel with probability 1/4. (a) Find the transition matrix for the chain. (b) Suppose the driver begins at the airport at time 0. Find the probability for each of his three possible locations at time 2 and the probability he is at hotel B at time 3. 6. The Markov chain of a manufacturing process goes as follows: A part to be manufactured
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Unformatted text preview: will begin the process by entering step 1. After step 1, 20% of the parts must be reworked; i.e., returned to step 1, 10% of the parts are thrown away and 70% proceed to step 2. After step 2, 5% of the parts must be returned to the step 1, 10% to step 2, 5% are scrapped, and 80% emerge to be solf for a proﬁt. Formulate a four state Markov chain with states 1,2,3,4 where 3=a part that was scrapped and 4=a part that was sold for a proﬁt. Give the transition matrix. 7. Consider a Markov chain on states { , 1 , 2 } with transition matrix P = . 3 . 3 . 4 . 2 . 7 . 1 . 2 . 3 . 5 . Compute P [ X 16 = 2 | X = 0] and P [ X 12 = 2 ,X 16 = 2 | X = 0]. Try not to do this by hand. 1...
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