Can you help me solve this Stochastic Question as soon as possible? Thanks so much!

8. (10 points) Let (Xn)n=0.1.2... be a Markov chain with transition graph 1/3 Q 1/3 2 3 1/3 (a) Provide the transition probability matrix P. (b) Is the Markov chain irreducible? Is the Markov chain aperiodic? Give a reason for your answers. (c) Compute for all i, je S = (1, 2,3} the limit lim pn n=00 Justify your answer! Does this limit depend on the initial starting value ?? (d) Let 72 := min{n > 1 : X, = 2). Compute E2[T2]