3. The Cov(X) of a random vector X'= (X₁, ..., Xn) is defined as E{(X-E(X))'(X-E(X)}. True or false, give reasoning.
3. The Cov(X) of a random vector X'= (X₁, ..., Xn) is defined as E{(X-E(X))'(X-E(X)}. True or false, give reasoning.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:3. The Cov(X) of a random vector X'= (X₁, ..., Xn) is defined as E{(X-E(X))'(X-E(X)}. True or false, give reasoning.
Expert Solution
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Step 1:-
We know that, X' is a vector and Covariance of a vector X is equal to the variance of X.
Which means,
Cov(X)= Var(X)
For a random variable,
Var(X)= E(X-E(X))2
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