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Suppose that where f= X ^N(μ, Σ) Σ = 12 -2 4 -2 6 4 -4 8

Suppose that where f= X ^N(μ, Σ) Σ = 12 -2 4 -2 6 4 -4 8

MATLAB: An Introduction with Applications
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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Suppose that where μ = 9 2 Χ ~ Ν.(μ,Σ) Σ = 12 4 -2 6 -4 4 8
Transcribed Image Text:Suppose that where μ = 9 2 Χ ~ Ν.(μ,Σ) Σ = 12 4 -2 6 -4 4 8
Suppose that X~ N₂(, ), where Σ has eigendecomposition Σ = QAQT. (a) What is the distribution of X-μ? (b) What is the distribution of Z = Q(X-μ)? (c) In terms of the eigenvalues of Σ, what is the expected value of ||Z||2= ZTZ, for Z as defined in (b)? (d) In terms of the eigenvalues of Σ, what is the expected value of ||X-μ||²?*
Transcribed Image Text:Suppose that X~ N₂(, ), where Σ has eigendecomposition Σ = QAQT. (a) What is the distribution of X-μ? (b) What is the distribution of Z = Q(X-μ)? (c) In terms of the eigenvalues of Σ, what is the expected value of ||Z||2= ZTZ, for Z as defined in (b)? (d) In terms of the eigenvalues of Σ, what is the expected value of ||X-μ||²?*
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