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Question 1 Consider a time-homogeneous Markov chain (Zn)new on the finite state S = {0, 1, 2, 3} with transition matrix 0.2 0 0.8 P = a b 0 0.3 where a, bER. 0 0 O 1. Determine all possible values for a, b such that P is a transition matrix Possible solutions: (a) a = 0.3, b = 0.4; (b) (a, b) E { (x, y) ER2 : x + y = 0.7}; ( c) ( a, b) E { ( x, y) E R2 : x t y = 0.7, x 2 0, y 2 0}; (d) (a, b) E {(x, y) ER2 : x ty = 0.7, x