Suppose that Y1 is the total time between a customers arrival in the store and departure

Chapter 5, Problem 5.33

(choose chapter or problem)

Suppose that Y1 is the total time between a customers arrival in the store and departure from the service window, Y2 is the time spent in line before reaching the window, and the joint density of these variables (as was given in Exercise 5.15) is f (y1, y2) = ey1 , 0 y2 y1 , 0, elsewhere. a Find the marginal density functions for Y1 and Y2. b What is the conditional density function of Y1 given that Y2 = y2? Be sure to specify the values of y2 for which this conditional density is defined. c What is the conditional density function of Y2 given that Y1 = y1? Be sure to specify the values of y1 for which this conditional density is defined. d Is the conditional density function f (y1|y2) that you obtained in part (b) the same as the marginal density function f1(y1) found in part (a)? e What does your answer to part (d) imply about marginal and conditional probabilities that Y1 falls in any interval?