Pattern Occurrences in Bernoulli Process. Let Yn denote a Bernoulli process with P{Y n = 1} = p and P{Yn = 0} = q = 1 − p. Suppose one is interested in the occurrence of a three-letter pattern in the...

Pattern Occurrences in Bernoulli Process. Let Yn denote a Bernoulli process with P{Y_n
= 1} = p and P{Yn = 0} = q = 1 − p. Suppose one is interested in the occurrence of a three-letter pattern in the sequence Y_n. Let X_n
= Y_n−2Y_n−1Y_n, for n ≥ 2. Show that X_n
is an ergodic Markov chain and find its stationary distribution