Please show the work thank you

Problem 6.4 (10 points) Consider the Markov chain X0, X1, X2, . . . with state space S = {1, 2, 3, 4, 5, 6, 7} and the following transition graph: 1/2 0.1 51 0 1/2 1 1 1/2 0.9 1 6 1/2 (a) Provide the transition matrix for this Markov chain. (b) Is there a limiting distribution? If so, determine it. (0) Determine the set of stationary distributions if any exist. If not, explain why