[See Steps] 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,
Question: 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 = weight of creams and Y =weights of the toffees and the pdf is described as: (20 pts)
\(f\left( x,y \right)=\left\{ \begin{aligned} & 24xy\,\,\,\,\,\,\text{for }0\le x\le 1,\,\,0\le y\le 1,\,\,x+y\le 1 \\ & 0\text{ elsewhere} \\ \end{aligned} \right.\)- Find the probability that in a given box, the cordials amount for more than half of the weight
- Find the marginal density for the weight of the creams
- Find the probability that the weight of the toffees in a box of less than 1/8 of a kilogram given that creams constitute ¾ of the weight
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