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Problem 7 10 points = 5 + 5] Consider a birth and death process, X = {X(t) : t> 0} with instant rates defined as follows: Ak = > and MK = k for k > 0. Parameter A has expected departure time in minutes as follows: E [So |X(0) = 0] = 20 1. Derive the limiting distribution, lim P[X(t) = k] t-+ 00 2. Evaluate the limiting expectation, lim E [X(t)]