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Unformatted text preview: and 2 if blue. The transition probability matrix is P = 1 / 5 4 / 5 2 / 7 3 / 7 2 / 7 3 / 9 4 / 9 2 / 9 The limiting probabilities are obtained from π = 1 / 5 π + 2 / 7 π 1 + 1 / 3 π 2 π 1 = 3 / 7 π 1 + 4 / 9 π 2 π + π 1 + π 2 = 1 which can be solved to get π = 25 / 89, π 1 = 28 / 89, π 2 = 36 / 89. 26. Let the state be the ordering of the deck of n cards, so there are n ! states. The transition probabilities are P ( i 1 , i 2 , · · · , i n ) , ( i j , i 1 , i 2 , · · · , i j1 i j +1 , · · · , i n ) = 1 n This Markov Chain is doubly stochastic, so in the limit all n ! states are equally likely. 2...
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 Spring '08
 Lim
 Operations Research, Probability theory, Stochastic process, Markov chain, Andrey Markov, Markov decision process, πi Pij

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