Answered>Order 298

Attaching the question below. Has to do with Markov chains and optimal prediction:

Consider a 2 state Markov chain X [k] with states {—1, 1} withtransition probability matrix dos dosa1==l?1 o9] Consider another 2 state Markov chain Z[k] with states {—1,1} withtransition probability matrix oas o4? A:2 lpas oas Assume that Z[k] and X[k] are statistically independent. Suppose weknow that at time I: = 4, Z[4] = 1 and X[4] = —1. LetM?=XM+ZM {a} Derive an optimal predictor for y[k] for times i: = 5,5, . . .. That isderive an expression for E{y[k] | X[4] = —1,E[4] = 1}, i: = 5,13, . . ..