Transition matrices and Markov Chain

1. Consider the following one-step transition matrix on the states {1, 2, 3, 4, 5, 6}: 10.20 00.80 0 2 0 0.1 0.3 0 0 0.6 P = 3 0 0.4 0 0 0 0.6 4 1 0 0 0 0 0 5 0.1 0.5 0.1 0 0 3 0 6 0 0.2 0.3 0 0 0.5 (a) Draw the transition diagram of the chain and identify its closed and irreducible sets. (b) Consider the two Markov chains whose transition matrices are: 2 0.1 0.3 0.6 (2::(0i2 068) and R=3 0.4 0 0.6 , 6 0.2 0.3 0.5 Compute the stationary distributions of Q and R. (c) Let (q1,q4) and (T2,?3,T5) denote the stationary distributions of Q and R from part (b). Show that 7r = (q1,0, 0,q4, 0,0) and 7r' = (0, r2, r3, 0, 0, T6) are both solutions to the system wP = 7r, and are therefore stationary distributions for P