2. Covariance matrix of temperature measurements in a weather = station, represented with a random vector X=[X₁ X2 X3]', is given as: Cx It is known that RVs X₁ are random Gaussian in nature 14 12.1 10.87 12.1 12 0 L10.8 0 11 a. What is the variance in these three measurements? Hint: Remember Cov(X,X)=Var(X) b. What are the Cov[X₁,X2] and Cov[X3, X1]? c. Are X₁ independent from one another?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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14
2. Covariance matrix of temperature measurements in a weather
station, represented with a random vector X=[X₁ X2 X3]', is given as: Cx = 12.1
It is known that RVs X₁ are random Gaussian in nature
L10.8
12.1 10.81
0
12
0
11
a.
What is the variance in these three measurements? Hint: Remember Cov(X,X)=Var(X)
b. What are the Cov[X₁,X₂] and Cov[X3,X1]?
C. Are X₁ independent from one another?
Transcribed Image Text:14 2. Covariance matrix of temperature measurements in a weather station, represented with a random vector X=[X₁ X2 X3]', is given as: Cx = 12.1 It is known that RVs X₁ are random Gaussian in nature L10.8 12.1 10.81 0 12 0 11 a. What is the variance in these three measurements? Hint: Remember Cov(X,X)=Var(X) b. What are the Cov[X₁,X₂] and Cov[X3,X1]? C. Are X₁ independent from one another?
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