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T= inf{n>0: Xn = Xo}. = (i)sism is a stationary distribut. al on Xo has the distribution (and

T= inf{n>0: Xn = Xo}. = (i)sism is a stationary distribut. al on Xo has the distribution (and

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
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Q 3. Let X = (Xn)n20 be a Markov chain with values in the finite state space S = {1,2,...,m}, and define T= = inf{n > 0: X = Xo}. Suppose that X is irreducible, and = (Ti)Isism is a stationary distribution of X. Let P, denote the probability measure P conditional on Xo has the distribution 7 (and similarly the expectation E). First show that ;> 0 for any 1≤ i ≤m, then compute ET. 05
Transcribed Image Text:Q 3. Let X = (Xn)n20 be a Markov chain with values in the finite state space S = {1,2,...,m}, and define T= = inf{n > 0: X = Xo}. Suppose that X is irreducible, and = (Ti)Isism is a stationary distribution of X. Let P, denote the probability measure P conditional on Xo has the distribution 7 (and similarly the expectation E). First show that ;> 0 for any 1≤ i ≤m, then compute ET. 05
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