The management at a fast-food outlet is interested in the joint behavior of the random variables...

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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 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 Y, includes the time a customer waits in line, we must have Y₁2 Ys. The relative frequency distribution of observed values of Y, and Y; can be modeled by the probability density function -{" e, 0≤ y ≤y < 00, elsewhere f(91.92)= with time measured in minutes. Find a P(Y, <2, Y₂ > 1). b P(₁ 22₂). c P(Y₁-Y₂21). (Notice that Y₁-Y₂ denotes the time spent at the service window.) 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 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 Y, includes the time a customer waits in line, we must have Y₁2 Ys. The relative frequency distribution of observed values of Y, and Y; can be modeled by the probability density function -{" e, 0≤ y ≤y < 00, elsewhere f(91.92)= with time measured in minutes. Find a P(Y, <2, Y₂ > 1). b P(₁ 22₂). c P(Y₁-Y₂21). (Notice that Y₁-Y₂ denotes the time spent at the service window.)

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