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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 Fall '10
 MenZhongxian
 Probability, Markov chain, symmetric random walk, equilibrium distribution, 1 j, unique equilibrium distribution

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