1. Consider the Markov chain with state 1, 2, 3, 4,5 and transition proba- bility matrix below. 0.5 0.5 0 0 0 0.5 0 05 0 0 P = 0 0 04 0.6 0 0 0 0 0.4 0.6 0 0 0.6 0 0.4 (a) State 1 is reachable from state(s) . , but not reachable from state(s) (b) State 3 communicates with state(s). but doesn't communi- cate with state(s) (c) State(s) form a closed set, state(s) form a non closed set. (d) This Markov chain is reducible / irreducible. (e) State(s) are transient, state(s) are recurrent. (f) State(s) are aperiodic, state(s) _ are periodic with a period of (g) This Markov chain is ergodic / not ergodic