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Problem 1: [15 points = 5 + 5 + 5] Hint: Exercise 6.4.2 from the textbook is important! Consider a small car service center that has n = 5 mechanics. The services are described as a birth-and- death process with instant rates per hour (), MK) defined as follows: Ak = 6 . (5 - k) and /k = 2 . k for 0 k = /k = 0 for k > 5. 1. Determine stationary (limiting as t -> co) distribution for the number of customers at the service center, WK = P[X(t) = k] for 0