Markov Chains Consider the Markov model with transition probabilities P(St+1|St) represented using the state transition diagram below. 20% 80% 20% a b 20% 60% 70% 30% (a) Write the state-transition probabilities as a 3x3 matrix M in which Ma,b P(b|a). (b) If the state is initially a (i.e., P(S1 = a) = 1), what is P(S3 = a)? (c) What is the stationary distribution of this Markov model?

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