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Problem 2: 15 points = [5 + 5 + 5] Consider a birth-and-death process, X = {X(t) : t> 0}, with instant rates Ax = > and /k = / per hour. You are given information about the expected departure times from states 0 and 1 as follows. . E [So |X(0) = 0] = 1 hour . E[S1 [X(0) = 1] = 12 minutes 1. Determine parameters ) and / 2. Derive the limiting distribution, my = lim P[X(t) = k] too for any k 2 0 3. Find the limiting expectation, lim E[X(t)] too