Given is the discrete-time Markov chain {Xn: n > 0} with state space S = and 1-step transition matrix P = --(141) = {1, 2, 3} At time 0 the Markov chain starts with probability 2/3 in state 1 and with probability 1/3 in state 2. a) [1 point] Determine the transient distribution at time 3. b) [1.5 points] What is the expected time until the Markov chain reaches state 3? c) [1.5 points] What is the total expected time spent in state 1 over an infinite horizon?