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Acandy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 3 kilograms, 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 shown below. Complete parts (a) through (c). ixy, 05x53, OsySS, x+ys3 f(x,y) = 27 0, elsewhere 2 (a) Find the probability that in a given box the cordials account for more than 5 of the weight. The probability is E. (Simplify your answer.) (b) Find the margina density for the weight of the creams. Select the correct choice below and ll in the answer box to complete your choice. O A. h(Y): O B. 90'): 1 3 (c) Find the probability that the weight of the toffees in a box is less than 3 of a kilogram if it is known that creams constitute E of the weight. The probability is E. (Simplify your answer.) Each rear tire on an experimental airplane is supposed to be lled to a pressure of 32 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 shown below. Complete parts (a) through (c). k x2+ , 27Sx 2}. (a) Complete the joint probability distribution below. (Type integers or simplified fractions.) X f ( x,y) 0 2 3 y 0 N (b) P[(X,Y)EA] = (Type an integer or simplified fraction.)