3. (16 points) Let (Yn)n1 be a sequence of i.i.d. random variables with P[Yn=1]=P[Yn=1]=41 and P[Yn=0]=21. Define Xn:=i=1nYi for all n1 and X0=1. (a) Explain why (Xn)n0 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 Pi,j(n) converges for n for all i and j in S, and determine the corresponding limits limnPi,j(n). (d) Find a stationary distribution for this Markov Chain..