Solved: A candy company distributes boxes of chocolates
Chapter 4, Problem 3.41(choose chapter or problem)
A candy company distributes boxes of chocolates with a mixture of creams, toees, and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toees, and cordials vary from box to box. For a randomly selected box, let X and Y represent the weights of the creams and the toees, 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, 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 toees in a box is less than 1/8 of a kilogram if it is known that creams constitute 3/4 of the weight.
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