1. Consider the Markov chain with the following transition matrix. 1/2 1/2 0 1/3 1/3 1/3 1/2 1/2 0 (a) Draw the transition diagram of the Markov chain. (b) Is the Markov chain ergodic? Give a reason for your answer. (c) Compute the two step transition matrix of the Markov chain. (d) What is the state distribution 7T2 for t = 2 if the initial state distribution for t = 0 is 770 = (0.3, 0.45, 0.25)T? 2. We continue to work with the Markov chain in Problem 1. (a) Find the rst passage probability ffl. (b) Find the rst passage probability f242. (0) Compute the average time \"1,1 for the chain to return to state 1. (d) Find the stationary distribution