2. Consider a Markov chain on states {0, 1, 2, 3, 4,...} with the transition probability matrix 0 1 2 3 4 0 1 — Po Po 0 0 0 1 1 — P1 0 P1 0 0 2 1 P2 : 0 0 P2 0 ... : : Determine if the Markov chain in each case below is transient or recurrent. (i) Pn = e−1/(n+1) for n = 0, 1, 2, … · ·; (ii) Pn = e−1/(n+1)² for n = 0, 1, 2, . · ·

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