Consider a Markov chain with two possible states s1 and s2 and with stationary transition probabilities as given in the following transition matrix P:
where the value of θ is unknown (0 ≤ θ ≤ 1). Suppose that the initial state X1 of the chain is s1, and let X2, . . . , Xn+1 denote the state of the chain at each of the next n successive periods. Determine the M.L.E. of θ based on the observations X2, . . . , Xn+1. |

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