5. On any given day Gary is either cheerful (C), so-so (S), or glum (G). If he is cheerful today, then he will be C, S, or G tomorrow with respective probabilities 0.5, 0.4, 0.1. If he is feeling so- so today, then he will be C, S, or G tomorrow with probabilities 0.3, 0.4, 0.3. If he is glum today, then he will be C, S, or G tomorrow with probabilities 0.2, 0.3, 0.5. Let X denote Gary's mood on the nth day, then {Xn, n 0} is a 3-state Markov chain (state 0 C, state 1 = S, state 2 = G) with transition probability matrix [0.5 0.4 0.1] P = 0.3 0.4 0.3 L0.2 0.3 0.5] = a) Gary is currently in a cheerful mood. What is the probability that he is not in a glum mood on any of the following three days? b) Gary was in a glum mood four days ago. Given that he hasn't felt cheerful in a week, what is the probability he is feeling glum today?