5. 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 - (24xy, 0s x< 1, 0

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
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Chapter9: Mass And Mass-related Variables In Engineering
Section: Chapter Questions
Problem 19P
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5. 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
- (24xy, 0s x< 1, 0<y<1,x+ y< 1,
0, elsewhere
f(x,y) =
(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.
Transcribed Image Text:5. 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 - (24xy, 0s x< 1, 0<y<1,x+ y< 1, 0, elsewhere f(x,y) = (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.
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