Let (Xn) be a Markov chain on a finite state space E with transition matrix II: EXE → → [0, 1]. Suppose that there exists a k EN such that II (x, y) > 0 for all x, y € E. For n € Z+ set Y₁ = (Xn, Xn+1). (1) Show that (Yn) is a Markov chain on E x E, and determine its transition matrix. (2) Does the distribution of Yn have a limit as n → [infinity]? If so, determine it.
