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Problem 8 [10 points = 5 + 5] Consider a birth and death process, X = {X (t) : t 2 0} with instant rates (per hour ) such that Ak = 2 for k = 0, 1, 2, and Ak = 0 for k 2 3, MK = k for k = 1,2 and /3 = 2, while /k = 0 for k > 3. 1. Derive the limiting distribution, lim P [X(t) = k] too 2. Find the limiting expectation, lim E[X(t)] t -+ 00