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 $.

Answered: 9. Let X be a three dimensional normal…

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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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