Question

(Q6) The management at a fast-food outlet is interested in the joint behaviour of the random variables Yı, defined as the total time between a customer's arrival at the store and departure from the service window, and Y2, the time a customer waits in line before reaching the service window. Because Yſ includes the time a customer waits in line, we must have Yi > Y. The relative frequency distribution of observed values of Yi and Y2 can be modelled by the probability density function f(yi, y2) = Se- y0 < y2 <yi< 00, 0. elsewhere with time measured in minutes. Find (a) P(Y1 < 2,Y2 > 1). (b) P(Y1 > 2Y2). (c) P(Yi - Y, > 1). (Notice that Y1 - Y, denotes the time spent at the service window.) (d) Find E(Y-Y) and Var(Y1 - Y). Is it highly likely that a randomly selected customer would spend more than 4 minutes at the service window?

Answer 1

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