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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).The amount of kerosene, in thousands of liters, in a tank at the beginning of any day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day so that x y, and assume that the joint density function of these variables is f(x, y) = (2, 0 2)