Consider the Markov chain (an = 0,1,2, . . .) with state space S = {1,2,3, 4} and transition matrix 0.3 0.7 0 0 0.2 0.2 0.5 0.1 0 0.4 0 0.6 0 0 0 1 (a) Draw the transition diagram for this Markov chain. (b) Find 1P(X2 = 2,X3 = 4|X0 = 2,X1 = 3). (c) What is P(X2 = 4, X1 = 4|X0 = 3)? ((1) Find the two-step transition probability p52) = 1? (X2 = 4 | X0 = 2). (9) Find h31 = 11:\"(Xn = 1 for some n 2 0 | X0 = 3), the probability of ever reaching state 1 starting from state 3