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.

Transcribed Image Text:

S1 S2 L3/4 1/4