(a) Compute the covariance matrix for the vector random variable. (b) Compute the eigenvectors of the covariance matrix. (c) Compute the KL-transform of x₁.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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T
Let X1 [1 2]¹, x₂ =
[2 1], x3 = [-1 0], x₁ = [0 −1]¹, x5 =
X3
X4
[0 −2]¹, x6 = [ -2 0], be samples of a two-dimensional vector random
variable. Do the following:
=
(a) Compute the covariance matrix for the vector random variable.
(b) Compute the eigenvectors of the covariance matrix.
(c) Compute the KL-transform of x₁.
Show all your computation steps. Do not use code for this problem.
Transcribed Image Text:T Let X1 [1 2]¹, x₂ = [2 1], x3 = [-1 0], x₁ = [0 −1]¹, x5 = X3 X4 [0 −2]¹, x6 = [ -2 0], be samples of a two-dimensional vector random variable. Do the following: = (a) Compute the covariance matrix for the vector random variable. (b) Compute the eigenvectors of the covariance matrix. (c) Compute the KL-transform of x₁. Show all your computation steps. Do not use code for this problem.
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