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Problem 6: 10 points Consider a birth-and-death process, X = {X(t) : t > 0} with two-state space, S = {0, 1}. The departure times are exponentially distributed with expectations shown in minutes as E [So |X(0) = 0] = = 12 and E[S1 |X(0) = 1] = 20 Derive the limiting distribution, To = lim P X(t) = 0] and 71 = lim P[X(t) = 1] t -+ 00