Please answer the question below and don't copy others, thank you!

Problem 2. Let (X,)", be a Markov chain on a finite state space E with transition matrix II : E x E -> [0, 1). Suppose that there exists a k ( N such that II" (a, y) > 0 for all c, y e E. For ne ZA set Yn := (X,, Xnti). (a) (8p) Show that (Y,, )",is a Markov chain on E x E, and determine its transition matrix. (b) (12p) Does the distribution of Y, have a limit as n -> co? If so, determine it