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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 f(z,y) = (x+2y). Ocxcl, Osys1, 10. alsowhere. a) Find the marginal density of X. b) Find the marginal density of Y. c) Find the probability that the drive-through facility is busy less than one-half of the time.A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees, and cordials vary from box to box. For a randomly selected box, let X and Y represent the weights of the creams and the toffees, respectively, and suppose that the joint density function of these variables is f(zy) = 10, elsewhere. a) Find the probability that in a given box the cordials account for more than 1/2 of the weight. b) Find the marginal density for the weight of the creams. c) Find the probability that the weight of the toffees in a box is less than 1/8 of a kilogram if it is known that creams constitute 3/4 of the weight.Let X and Y denote the lengths of life, in years, of two components in an electronic system. If the joint density function of these variables is (e ( +). 130, y>0. f(x, y) = 10, elsewhere, find P(0 0, y>0. elsewhere, Find -(sty), r>0, y>0. f(x, y) = 10. elsewhere,Each rear tire on an experimental airplane is supposed to be filled to a pressure of 40 pounds per square inch (psi). Let X denote the actual air pressure for the right tire and Y denote the actual air pressure for the left tire. Suppose that X and Y are random variables with the joint density function f(x, y) = 10. [k(x + y'), 30 5 x