4. 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(x, y) = (24xy. 0≤x≤ 1,0 ≤ y ≤ 1,x + y ≤ 1, elsewhere. 0, (1) Find the probability that in a given box the cordials account for more than 1/2 of the weight. (2) Find the marginal probability densities of X and Y, and determine whether or not X and Y are independent. 3) Find the probability that the weight of the toffees in a box is less than 1/8 of a

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