Consider a Markov chain {X,:n>0} with transition probability matrix: 1 2 3 4 states 0.3 0.7 1 P= 2 0.8 0.2 0.5 0.5 3 0.9 0.1 4 0.1 0.2 0 0.3 0.4 The limiting TT's are: TTo = 29 / 80, TI = 11 / 80, T2 = 7/ 32, TT3 = 9/ 32, TT4= 0 a) Determine the classes of this Markov chain. For each class state whether the class is transient or recurrent. Also, state the period of each class. CLASS PERIOD TRANSIENT or RECURRENT b) If we start in state 2, on average, how many transitions will it take to return to Express as an exact fraction. state 2?

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