Probability

Marginal density

A candy company distributes boxes of choco- lates 1With a mixture of creams, toifees, and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees, and cor dials 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 _ 24:529. 05351, 051151, m+ySL f(a:, y) _ {0, 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 tu'eee in a box is less than 1/8 of a kilograin if it is known that creams constitute 3/ 4 of the weight