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Unformatted text preview: 9. Consider a Markov chain with state space S = { , 1 , . . ., 7 } and transition matrix 1 / 2 1 / 4 1 / 4 1 / 4 3 / 4 1 / 3 2 / 3 1 / 5 1 / 5 1 / 5 1 / 5 1 / 5 1 / 6 1 / 3 1 / 6 1 / 6 1 / 6 1 1 / 4 3 / 4 2 / 3 1 / 3 (a) Determine the classes of this chain, and organize the matrix into simple form. Which states are transient? Determine the period of each class. (b) Find the equilibrium distribution corresponding to each closed class, and write down the general form of all equilibrium distributions for this chain. (c) Find the absorption probability from each transient state into each closed class. (d) If X = 0, describe the longrun behavior of this chain. Do the same for X = 3. 1...
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This note was uploaded on 01/19/2011 for the course STATISTICS STAT 333 taught by Professor Menzhongxian during the Fall '10 term at Waterloo.
 Fall '10
 MenZhongxian
 Probability

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