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Problem 8 [10 points = 5 + 3 + 2] Consider a small barber shop with three masters, which is described in terms of a birth and death process, X = {X(t) : t > 0}, having instant rates {Ax =9: 0 3. 1. Derive the stationary (limiting) distribution for a number, X (t) of customers at time t. 2. Find the queue length, L 3. Determine the proportion of time when X (t) = 0. Equivalently, find the stationary probability of the event (X (t) = 0)