The management at a fast-food outlet is interested in the joint behavior of the random variables Y1, defined as the total time between a customers 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 Y1 includes 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 f (y1, y2) = ey1 , 0 y2 y1 < , 0, elsewhere with time measured in minutes. Find a P(Y1 < 2, Y2 > 1). b P(Y1 2Y2). c P(Y1 Y2 1). (Notice that Y1 Y2 denotes the time spent at the service window.)

Introduction: Conducting a Research Observational study: without attempting to influence the value of response or explanatory variables. Observes behavior. Designed Experiment Study: assigns to a certain group of individuals intentionally changes value of explanatory variable and records the value of the response variable of each group. Population: entire group of individuals to be studies...