A Markov chain has state space Z= {0, 1,2,3,4} and transition matrix 0 1 0 0 0 1 0 0 0 0 P = 0.2 0.2 0.2 0.4 0 0.2 0.8 0 0 0 0.4 0.1 0.1 0 0.4 (1) Find the essential and inessential states. (2) Find the recurrent and transient states.