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Problem 7.3 (10 points) Consider a Markov chain on the state space S = {0, 1, 2, 3, ...} with the transition matrix 1/2 1/2 0 0 O 2/3 0 1/3 0 0 3/4 0 0 1/4 0 . . . P = 4/5 0 0 0 1/5 . . . 5/6 0 0 0 0 . . . . . . . . . . . . That is, for any i > 0, Pi,j = (i + 1)/(2 + 2) if j = 0, Pi,j =1/(2 + 2) if j = i + 1 and Pi,j = 0 otherwise. Page 2 of 3 PSTAT 160A ASSIGNMENT 7 (a) (5 points) Determine if this chain is irreducible and classify each state as either transient or recurrent. (b) (5 points) Let T3 be the first hitting time of state 3. Using first-step analysis, determine Eo[3], expected time to reach state 3 for the first time, starting at state 0