Let X,, be a Markov chain on the states {1, 2, 3, 4} with transition matrix 1 0 0 0 1/3 0 2/3 0 0 1/2 0 1/2 0 0 0 1 P = (a) Find the equivalence classes of this Markov chain. (b) Find the periods of the equivalence classes. () Which of the equivalence classes are recurrent? transient? (d) Let ay be the absorption probability in state 4 if we start from state i. Find a;4 for i=2.3. (e) Let pu; be the expected time until the chain hits state 1 or state 4, given that Xy = i. Find ps and pg