Would appreciate it if you're able to answer it. 

Consider the Markov chain Xn which has transition matrix given by 1/2 1/2 0 0 0 1/2 0 1/2 0 0 P: 0 1/2 0 1/2 0 0 0 1/2 0 1/2 0 0 0 1/2 1/2 (a) Draw the graph of this Markov chain and determine the communicating classes. Which classes are recurrent and which are transient? (b) Find all stationary distributions of this Markov chain. (c) Write code that samples the rst 250 steps of the chain: (X0, . . . ,X250) where X0 starts at whichever state you choose. (do not print this) (d) Compute the proportion of time that the chain spends in each of the states in your simulation. Print out your code with this output. (e) Does your answer to the last part of the problem make sense to you? Explain why you got the answer that you got