Question: Consider a Markov chain with two possible states, S = {0, 1}. In particular, suppose that the transition matrix is given by where a and

Consider a Markov chain with two possible states, S = {0, 1}. In particular, suppose that the transition matrix is given byP = 1-a a b 1-b

where a and b are two real numbers in the interval [0, 1] such that 0

where α ∈ [0, 1].

a. Using induction (or any other method), show thatpn = Pn b a 1 a+bb a + (1-a-b)n a+b a -b b

b. Show thatlim Pn = pn n 1 b +[a] a+b b

c. Show thatlim 7(n) n [+] = a+b a+b

P = 1-a a b 1-b

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