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Problem 1: 15 points = [5 + 5 -| 5] Consider a birth and death process, X = {X (t) : t 2 0}. Its instant rates are M = 6 per hour and pk = 10 per hour 1. For any 16 2 0, derive the limiting distribution, lim P [X(t) : 1:] 11300 2. Evaluate the limiting expectation, lim E[X(t)] t>oo 3. Find conditional expected value E [30 |X(0) = 0] 0f the departure time from the state X (0) = 0