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Problem 2 [15 points = 5 + 5 + 5] Consider a queuing system M /M / 1 with single server that is functioning under stationary distribution. Customer arrivals form a Poisson process with sojourn times {83; : j 2 1} being exponentially distributed with E [83-] = 10 minutes. Service times are independent exponentially distributed with average : u'1 = 6 minutes. 1. Derive stationary (limiting) distribution for X (t) and present it as probabilities ark : lim P [X(t) = k] t)OO for all integer k 2 0 2. Find expected waiting time (W), for a customer in minutes 3. Evaluate average queue length, L = E [X(t)] under stationary distribution