I be a 4-dimensional random vector defined as X = = ation matrix E[X] = at V 0 0 be a 3-dimensional random vector with Rx = X₁ X₂ 1 -1 0 0 Y₁ = X₁ - X2, Y2=X2- X3, Y3 = X3 - X4. -1 0
I be a 4-dimensional random vector defined as X = = ation matrix E[X] = at V 0 0 be a 3-dimensional random vector with Rx = X₁ X₂ 1 -1 0 0 Y₁ = X₁ - X2, Y2=X2- X3, Y3 = X3 - X4. -1 0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Let X be a 4-dimensional random vector defined as X =
correlation matrix
E[X]
=
0
0
0
0
Let Y be a 3-dimensional random vector with
Rx =
[X₁ X2 X3 X4]' with expected value vector and
1
0
0
Y₁ = X₁ - X2,
Y₂=X2- X3,
Y3 = X3 X4.
-1
7
1
-1
0
0
-1
1
(a) Find a matrix A such that Y = AX.
(b) Find the correlation matrix of Y, that is Ry.
(c) Find the correlation matrix between X₁ and Y, that is Rx₁Y.
0
0
-1
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e175be6-c4c9-439e-aff9-c884de3cc560%2F2ba575ff-6beb-4da8-b594-5ffd977058bd%2Fqn9rfp_processed.png&w=3840&q=75)
Transcribed Image Text:Let X be a 4-dimensional random vector defined as X =
correlation matrix
E[X]
=
0
0
0
0
Let Y be a 3-dimensional random vector with
Rx =
[X₁ X2 X3 X4]' with expected value vector and
1
0
0
Y₁ = X₁ - X2,
Y₂=X2- X3,
Y3 = X3 X4.
-1
7
1
-1
0
0
-1
1
(a) Find a matrix A such that Y = AX.
(b) Find the correlation matrix of Y, that is Ry.
(c) Find the correlation matrix between X₁ and Y, that is Rx₁Y.
0
0
-1
1
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