2. Which of the following transition matrices belong to regular Markov chains? Find a stable distribution for each chain. (a) (b) 0 OH OH only 10 (c) 0 0 1 00

4. Let (X₂)o be a Markov chain with state space S = {1,2,3} and transition matrix .8 .2 O .5 .5 0 0 0 1 Find two different stationary distributions for this Markov chain. P =

2. Consider a Markov chain (Xn) with state space S = {1, 2, 3, 4, 5} and transition matrix 0.5 0.5 0 0 0 0.4 0.6 0 0 0 P = 0 0.3 0.3 0.4 0 0 0 0 0.6 0.4 000 0.6 0.4 One stationary distribution for this Markov chain is (4, 5, 0, 0, 0). Suppose the Markov chain (X) is started from the initial distribution λ = (0.1 0 0.7 0.2 0). What are the limiting probabilities limn→∞ P(X = i) for each i € S?

2.5 10. pls help