9. Let X be a three dimensional normal with mean and covariance -(0) fl= 2 1 1 3 -1 2 == (1 Σ Set Y₁ = X₁ + X2 + X3 and Y2 = X1 + X3. Determine the conditional distribution of Y₁ given that Y₂ = 0
9. Let X be a three dimensional normal with mean and covariance -(0) fl= 2 1 1 3 -1 2 == (1 Σ Set Y₁ = X₁ + X2 + X3 and Y2 = X1 + X3. Determine the conditional distribution of Y₁ given that Y₂ = 0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Let \( X \) be a three-dimensional normal vector with mean vector \(\mu\) and covariance matrix \(\Sigma\) given by:
\[
\mu = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}
\]
\[
\Sigma = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 3 & -1 \\ 1 & -1 & 2 \end{pmatrix}
\]
Define the variables \( Y_1 \) and \( Y_2 \) as follows:
- \( Y_1 = X_1 + X_2 + X_3 \)
- \( Y_2 = X_1 + X_3 \)
The task is to determine the conditional distribution of \( Y_1 \) given that \( Y_2 = 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5faf6c58-f50a-4c20-bd5e-98fe14144213%2Fc5c7fe4b-29dc-4655-a0c9-3ac61ffd32aa%2Fe94hzuj_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( X \) be a three-dimensional normal vector with mean vector \(\mu\) and covariance matrix \(\Sigma\) given by:
\[
\mu = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}
\]
\[
\Sigma = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 3 & -1 \\ 1 & -1 & 2 \end{pmatrix}
\]
Define the variables \( Y_1 \) and \( Y_2 \) as follows:
- \( Y_1 = X_1 + X_2 + X_3 \)
- \( Y_2 = X_1 + X_3 \)
The task is to determine the conditional distribution of \( Y_1 \) given that \( Y_2 = 0 \).
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