Consider the Markov chain with following transition matrix P: 0.5 0 0.5 0 0 0.5 0 0.5 0.5 0.25 0 0.25 0 1 0 0 P: (a) Draw the transition diagram. closed. (c) Identify positive recurrent, null recurrent, and transient states. (d) Is the Markov chain irreducible? Give reasons for your answer. (e) Is the Markov chain ergodic? Give reasons for your answer. (f) Identify essential and inessential states. (g) Give the 2step transition matrix