3.41 A candy company distributes boxes of choco- lates 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 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 [24xy, 0≤x≤ 1,0 ≤ y ≤ 1, x+y≤l, elsewhere. f(x, y) = (0,
3.41 A candy company distributes boxes of choco- lates 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 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 [24xy, 0≤x≤ 1,0 ≤ y ≤ 1, x+y≤l, elsewhere. f(x, y) = (0,
3.41 A candy company distributes boxes of choco- lates 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 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 [24xy, 0≤x≤ 1,0 ≤ y ≤ 1, x+y≤l, elsewhere. f(x, y) = (0,
All I need help with is putting this function on a calculator Ti-89 Platinum. The answer is -2/75 but I don’t know how to put that in the calculator and get it right. Please help.
Transcribed Image Text:**Transcription for Educational Website:**
**Question**
**4.83** Referring to the random variables whose joint density function is given in Exercise 3.41 on page 105, find the covariance between the weight of the creams and the weight of the toffees in these boxes of chocolates.
**3.41** 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
\[
f(x, y) =
\begin{cases}
24xy, & 0 < x \leq 1, \ 0 \leq y \leq 1, \ x + y \leq 1, \\
0, & \text{elsewhere.}
\end{cases}
\]
The problem is accompanied by a mathematical function which describes the joint probability of the weights of creams (\(X\)) and toffees (\(Y\)) in a randomly selected box of chocolates. The region of support for this joint density function is restricted to values of \(x\) and \(y\) such that \(0 < x \leq 1\), \(0 \leq y \leq 1\), and \(x + y \leq 1\). Outside of this defined domain, the function is zero.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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![**Transcription for Educational Website:**
**Question**
**4.83** Referring to the random variables whose joint density function is given in Exercise 3.41 on page 105, find the covariance between the weight of the creams and the weight of the toffees in these boxes of chocolates.
**3.41** 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
\[
f(x, y) =
\begin{cases}
24xy, & 0 < x \leq 1, \ 0 \leq y \leq 1, \ x + y \leq 1, \\
0, & \text{elsewhere.}
\end{cases}
\]
The problem is accompanied by a mathematical function which describes the joint probability of the weights of creams (\(X\)) and toffees (\(Y\)) in a randomly selected box of chocolates. The region of support for this joint density function is restricted to values of \(x\) and \(y\) such that \(0 < x \leq 1\), \(0 \leq y \leq 1\), and \(x + y \leq 1\). Outside of this defined domain, the function is zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d7ec503-389e-4b40-b2fe-31c0ac723423%2Fbe2a19ac-d5bd-4e90-a8be-30fd93a5c7d7%2Fciumk8b_processed.jpeg&w=3840&q=75)
