solve these questions:

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,Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density f (r, y) = 01/2).Referring to Exercise 3.38, find (a) the marginal distribution of X; (b) the marginal distribution of Y Reference: Exercise 3.38: If the joint probability distribution of X and Yis given by f(x, y) = 30 for x = 0, 1, 2, 3; y = 0, 1, 2, find a) P(X 2, Y= 1); c) (c) P(X >Y):(d) P(X + Y = 4)