Question

2. Let $Y_1$ and $Y_2$ be as in Problem 2. Let $\ egin{aligned} mathbf{C} = egin{pmatrix} c_{11} & c_{12} \ c_{21} & c_{22} end{pmatrix}. end{aligned}$ (a) Find $mathbf{C}mathbf{Y}$ and $var(mathbf{C}mathbf{Y})$ using the definition of covariance. (b) By doing the matrix multiplication $mathbf{C}mathbf{Sigma}mathbf{C}'$, show that $var(mathbf{C}mathbf{Y}) = mathbf{C}mathbf{Sigma}mathbf{C}'$, where $mathbf{Sigma}$ is the matrix you found in Problem 1(b).

          2. Let $Y_1$ and $Y_2$ be as in Problem 2. Let
$\
egin{aligned}
mathbf{C} = egin{pmatrix}
 c_{11} & c_{12} \
 c_{21} & c_{22}
end{pmatrix}.
end{aligned}$

(a) Find $mathbf{C}mathbf{Y}$ and $var(mathbf{C}mathbf{Y})$ using the definition of covariance.

(b) By doing the matrix multiplication $mathbf{C}mathbf{Sigma}mathbf{C}'$, show that $var(mathbf{C}mathbf{Y}) = mathbf{C}mathbf{Sigma}mathbf{C}'$, where $mathbf{Sigma}$ is the matrix you found in Problem 1(b).

2. Let Y1 and Y2 be as in Problem 2. Let
eginaligned
mathbfC = eginpmatrix
c11 c12 c21 c22
endpmatrix.
endaligned

(a) Find mathbfCmathbfY and var(mathbfCmathbfY) using the definition of covariance.

(b) By doing the matrix multiplication mathbfCmathbfSigmamathbfC', show that var(mathbfCmathbfY) = mathbfCmathbfSigmamathbfC', where mathbfSigma is the matrix you found in Problem 1(b).

Added by Destiny A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Dominador Tan

02/23/2024

Step 1

From Problem 2, we have: Y = \begin{bmatrix} Y_1 \\ Y_2 \end{bmatrix} = C \begin{bmatrix} X_1 \\ X_2 \end{bmatrix} Now, we are given the matrix C: C = \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix} So, we can find Y as: Y = \begin{bmatrix} Show more…

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2. Let Y1 and Y2 be as in Problem 2. Let C = (c11 c12 c21 c22). (a) Find CY and var(CY) using the definition of covariance. (b) By doing the matrix multiplication CΣC', show that var(CY) = CΣC', where Σ is the matrix you found in Problem 1(b).