If Y, is the total time between a customer's arrival in the store and departure from the servicewindow and if Y2 is the time spent in line before reaching the window, the joint density of thesevariables isf\V1. Y2) =se-y1, 0< y2 < y1 <00,elsewhere.%3DThe random variable Y, – Y2 represents the time spent at the service window.Find E (Y, - Y,2). [Hint: Y, has a gamma distribution with a = 2 and B = 1, and Y, has anexponential distribution with ß = 1]

If Y, is the total time between a customer's arrival in the store and departure from the service window and if Y2 is the time spent in line before reaching the window, the joint density of these variables is f(y1» Y2) = {0, 0 y2 s y1 s 00, %3D elsewhere. The random variable Y, – Y2 represents the time spent at the service window. Find E (Y, - Y,). [Hint: Y, has a gamma distribution with a = 2 and B = 1, and Y, has an exponential distribution with ß = 1]