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 toffee, respectively, and suppose that the joint density function of these variables is 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 toffee, respectively, and suppose that the joint density function of these variables is
f(x,y)=24xy, for 0≤x≤1, 0≤y≤1, x+y≤1
f(x,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 toffees in a box is less than 1/8 of a kilogram if it is known that creams constitute 3/4 of the weight.