Question: Problem 8 (10 points = 5 + 5] Consider a birth and death process, X = {X(t): t2 0} with instant rates (per hour) such

Problem 8 (10 points = 5 + 5] Consider a birth and death process, X = {X(t): t2 0} with instant rates (per hour) such that tx = 2 for k=0,1,2, and =0 for k 23, Hk = k for k= 1,2 and pug = 2, while pik = 0 for k > 3. 1. Derive the limiting distribution, #1 = lim P[X(t) = k] 2. Find the limiting expectation, lim E(XO)] t-00 Solution Problem 8 (10 points = 5 + 5] Consider a birth and death process, X = {X(t): t2 0} with instant rates (per hour) such that tx = 2 for k=0,1,2, and =0 for k 23, Hk = k for k= 1,2 and pug = 2, while pik = 0 for k > 3. 1. Derive the limiting distribution, #1 = lim P[X(t) = k] 2. Find the limiting expectation, lim E(XO)] t-00 Solution

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