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Zero-mcan gaussian random variables X1, X2, and X, having a covariance matrix 4 2.05 1.05 [C:] = 2.05 1.05 2.05 4 2.05 4 arc transformed to new variables Y, = 5X1 +2X2 – X3 Y2 = -X, +3X2 +X3 Y3 = 2X1 -- X2 + 2X3 (a) Find the covariance matrix of Y1, Y2, and Y3. (b) Write an expression for the joint density function of Y, Y2, and Y3.

Zero-mcan gaussian random variables X1, X2, and X, having a covariance matrix 4 2.05 1.05 [C:] = 2.05 1.05 2.05 4 2.05 4 arc transformed to new variables Y, = 5X1 +2X2 – X3 Y2 = -X, +3X2 +X3 Y3 = 2X1 -- X2 + 2X3 (a) Find the covariance matrix of Y1, Y2, and Y3. (b) Write an expression for the joint density function of Y, Y2, and Y3.

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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Zero-mcan gaussian random variables X1, X2, and X, having a covariance matrix 4 2.05 1.05 [C:] = 2.05 1.05 2.05 4 2.05 4 arc transformed to new variables Y, = 5X1 +2X2 – X3 Y2 =-X1 +3X2 +X3 Y3 = 2X1 - X2 + 2X3 (a) Find the covariance matrix of Y1, Y2, and Y3. (b) Write an expression for the joint density function of Y, Y2, and Y3.
Transcribed Image Text:Zero-mcan gaussian random variables X1, X2, and X, having a covariance matrix 4 2.05 1.05 [C:] = 2.05 1.05 2.05 4 2.05 4 arc transformed to new variables Y, = 5X1 +2X2 – X3 Y2 =-X1 +3X2 +X3 Y3 = 2X1 - X2 + 2X3 (a) Find the covariance matrix of Y1, Y2, and Y3. (b) Write an expression for the joint density function of Y, Y2, and Y3.
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