Unformatted text preview: E i T i = 1 /π ( i ). (c) Use (a) to prove E i ( T i ) 2 = 2 E i T i ( X j ( E j T i /E j T j )1) . 5. Let ( X n ; n ≥ 0) be a ﬁnitestate irreducible Markov chain. Write π for the stationary distribution and T j = min { n ≥ 0 : X n = j } for the ﬁrst hitting time. (a) Prove that ∑ j π j E i T j does not depend on i . (b) Give an example to show that ∑ i π i E i T j may depend on j . 5...
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 Spring '09
 Reed
 Markov chain, Xn, Ei Tj

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