Problem 3.5. Consider a CTMC {Xt} on S = {1, 2, 3, 4} with generator matrix 3 0 N 2 Q = -3 2 2 -5 Note that Q can be diagonalized as Q = UDU-, where 0 3 -2 -6 0 O -1/4 1/4 0 0 -1/5 2/5 0 -1/5 1 3 U = D = U 1 = 0 1/4 -1/8 -1/4 1/8 -3 0 1/4 9/40 O 0 7/20 7/40 5 3 Let P(t) denote the transition function of {Xt}. Does P(t) converge as t - co? If so, what is the limit