Please help!!!

4. (20 points) Consider a discrete time Markov chain X = {X. :n =0, 1...} on state space { 1, 2,3,4,5,6} with transition matrix 0 O 0 P = 0 0 0.6 0 0 0.6 0.4 0 0 0 0.4 0. 0 0 0 0 Its diagram is as follows: 5 (a) (4 points) Consider irreducible subset {1,2}, is it recurrent or positive recurrent or transient? What is its period? (b) (6 points) Please find another irreducible subset other than {1,2}. Is it recurrent or positive recurrent or transient? What is its period? (c) (4 points) Find lim, ,-Pr{X = 3 Xo = 2}