7.21 A particular fast-food outlet is interested in the joint behavior of the random variables Y1, the total time between a customer’s arrival at the store and his leaving the service window, and Y2, the time that the customer waits in line before reaching the service window. Since Y1 contains the time a customer waits in line, we must have Y1 Y2. The relative frequency distribution of observed values of Y1 and Y2 can be modeled by the probability density function a Find P(Y1  2, Y2  1).
b Find P(Y1 2Y2).
c Find P(Y1  Y2 1). [Note: Y1  Y2 denotes the time spent at the service windows.]
d Find the marginal density functions for Y1 and Y2.