Linear programming problem. Please include all the steps.

2 (5 points). The transition matrix of a Markov chain on a state space of three elements is given as [1/3 1/3 1/3] P = 2/3 0 1/3 1/3 2/3 0 (a) Sketch a transition diagram for the Markov chain. (b) Find the steady-state distribution of the states by solving the eigenvector problem Pry = v. (c) Let f(X) be a function of the random variable X E S = {0, 1, 2} be defined as f(0) = -1, f (1) = 0, f(2) = 1. What is the expected mean value of f, i.e. E(f)