(16 points) Let (Y),21 be a sequence of i.i.d. random variables with P[Y, = 1] = P[Y, = -1] = = and P[Yn = 0] = =. Define Xn := [TRY; for all n 2 1 and Xo = 1. (a) Explain why (Xn )man is a Markov chain and provide the corresponding transition matrix P and transition graph. (b) Determine the communication classes and their periodicity. (c) Argue that p(n) converges for n - co for all i and j in S, and determine the corresponding limits lim, - p(n) (d) Find a stationary distribution for this Markov Chain