Question

T 12 X=(X?,X?)~N?(?,c); 2 Let 3 1 2 ?=\begin{bmatrix} 3\\5\end{bmatrix},c=\begin{bmatrix} 1 & 2\\1 & 4\end{bmatrix}. 5 1 4 Y=AX+b; Let 3 1 7 A=\begin{bmatrix} 3 & 1\\0 & 2\end{bmatrix},b=\begin{bmatrix} 7\\2\end{bmatrix}. 0 2 2 Then covariance matrix of Y is:

          T
12
X=(X?,X?)~N?(?,c);
2
Let
3
1 2
?=\begin{bmatrix} 3\\5\end{bmatrix},c=\begin{bmatrix} 1 & 2\\1 & 4\end{bmatrix}.
5
1 4
Y=AX+b;
Let
3 1
7
A=\begin{bmatrix} 3 & 1\\0 & 2\end{bmatrix},b=\begin{bmatrix} 7\\2\end{bmatrix}.
0 2
2
Then covariance matrix of Y is:

T
12
X=(X?,X?) N?(?,c);
2
Let
3
1 2
?=
< b m a t r i x >
,c=
< b m a t r i x >
.
5
1 4
Y=AX+b;
Let
3 1
7
A=
< b m a t r i x >
,b=
< b m a t r i x >
.
0 2
2
Then covariance matrix of Y is:

Added by Consuelo I.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Dominador Tan

02/03/2024

Step 1

Step 1: We know that $Cov(Y) = A Cov(X) A^T$. Show more…

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$X = (X_1, X_2)^T \sim N_2(\mu, c);$ Let $\mu = \begin{bmatrix} 3 \\ 5 \end{bmatrix}, c = \begin{bmatrix} 1 & 2 \\ 1 & 4 \end{bmatrix}$. $Y = AX + b;$ Let $A = \begin{bmatrix} 3 & 1 \\ 0 & 2 \end{bmatrix}, b = \begin{bmatrix} 7 \\ 2 \end{bmatrix}$. Then covariance matrix of Y is: