4. (18 pts.] A cereal manufacturer is aware that the weight of the product in the box varies slightly from box to box. In fact, considerable historical data have allowed the determination of the density function that describes the probability structure for the weight of the product in weight product in box (in box (in ounces). Letting X be the lom varia ounces), the density function can be described as: 3

A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is fxy (x, y) = 091 to (r +2y), Or