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April 30th, 2007, 04:57 PM   #1
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markov chains

Is the following true or false, and why?

E_x { 1_y (X_n) } = P^n (x,y)
"The expected value, given a markov chain started in state x at time 0, of the indicator function (i.e. 1_y (Z) = 1 if Z=y and 0 if otherwise) on X_n, the state that the markov chain is in at time n,
is equal to the probability that the markov chain will get from state x to state y in n steps."
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