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Let X be a Gaussian random vector with distribution [5 4 ~~ (B]. []). 5 X~N Let Ỹ be a Gaussian random vector formed by multiplying ✈ by a certain matrix: M-HN Find the mean vector of Y.

Let X be a Gaussian random vector with distribution [5 4 ~~ (B]. []). 5 X~N Let Ỹ be a Gaussian random vector formed by multiplying ✈ by a certain matrix: M-HN Find the mean vector of Y.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let \(\vec{X}\) be a Gaussian random vector with distribution \[ \vec{X} \sim \mathcal{N} \left( \begin{bmatrix} 3 \\ 5 \end{bmatrix}, \begin{bmatrix} 5 & 4 \\ 4 & 5 \end{bmatrix} \right). \] Let \(\vec{Y}\) be a Gaussian random vector formed by multiplying \(\vec{X}\) by a certain matrix: \[ \begin{bmatrix} Y_1 \\ Y_2 \\ Y_3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 1 & 1 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} X_1 \\ X_2 \end{bmatrix}. \] Find the mean vector of \(\vec{Y}\).
Transcribed Image Text:Let \(\vec{X}\) be a Gaussian random vector with distribution \[ \vec{X} \sim \mathcal{N} \left( \begin{bmatrix} 3 \\ 5 \end{bmatrix}, \begin{bmatrix} 5 & 4 \\ 4 & 5 \end{bmatrix} \right). \] Let \(\vec{Y}\) be a Gaussian random vector formed by multiplying \(\vec{X}\) by a certain matrix: \[ \begin{bmatrix} Y_1 \\ Y_2 \\ Y_3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 1 & 1 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} X_1 \\ X_2 \end{bmatrix}. \] Find the mean vector of \(\vec{Y}\).
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