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 is unknown (0 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 based on the observations X2, , Xn 1 S1 S2 L3 4 1 4

Question: 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

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 Î¸ is unknown (0 ‰¤ Î¸ ‰¤ 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 Î¸ based on the observations X2, . . . , Xn+1.

S1 S2 L3/4 1/4

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