Letting X denote Gary's mood on the nth day, then {Xn, n ≥ 0} is a three-state Markov chain (state 0 = C, state 1 = :S, state 2 G) with transition probability matrix = P = 0.5 0.4 0.1 0.3 0.4 0.3 0.2 0.3 0.5