Question

Consider the Markov chain X₀,X₁,X₂,... on the state space S = {0,1} with transition matrix

P=$\begin{bmatrix} \alpha & 1-\alpha \\ 1-\beta & \beta \end{bmatrix}$

(a) Show that the process defined by the pair Z_n := (X_n−1,X_n), n ≥ 1, is a Markov chain on the state space consisting of four (pair) states: (0,0),(0,1),(1,0),(1,1).

(b) Determine the transition probability matrix for the process Z_n, n ≥ 1.

Answer 1

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