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

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 Zn := (Xn−1,Xn), 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 Zn, n ≥ 1.

math   Statistics-And-Probability   
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