Question: Please answer the question below and don't copy others, thank you! Problem 3 (20p). For each j ( Z. let r; ( [0, co) be

Please answer the question below and don't copy others, thank you!

Problem 3 (20p). For each j ( Z. let r; ( [0, co) be given. Let (X,)me, be a Markov chain on E :=Zy with transition matrix II : E x E -> [0, 1] given by e -Tj if k = j +2, II(j, k) = 1-e Ti if k = 0, otherwise. Suppose that _ _12; = co. Determine whether the state 0 is recurrent or transient

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