Question no. 24 A Markov chain with state space {-2,-1,0, 1, 2} has the following one- step transition probabilities: Pi,i+1=3/4 for i = -2,-1,0,1 Pi,i-1=1/4 for i = -1,0, 1,2 P-2,2 = 1/4 = 1-P2.-2 (a) Determine the classes of the Markov chain. For each class, establish whether it is recurrent or transient and whether it is periodic or aperiodic. (b) Do the limiting probabilities exist? If they do, compute them. (c) Is the chain time-reversible (see p. 147)? Justify.

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