Question: Consider a discrete-time Markov chain with state space S = {0, 1} and write the transition probability matrix 1-a a b 1 -b Assume further

Consider a discrete-time Markov chain with state space S = {0,

Consider a discrete-time Markov chain with state space S = {0, 1} and write the transition probability matrix 1-a a b 1 -b Assume further that the initial distribution a = Pr (Xo =0) =1 - Pr (Xo = 1). (a) (10 pts). Find Pr (X1 # X2) in terms of a, a and b. (b) (15 pts). Show that b Pr (Xn+1 = 0) b atb = (1 -a - b) . Pr (X, = 0) - a+bl and then conclude b Pr (Xn = 0) = +(1-a-b) a b ath atb

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