Explanation Given info: X is a random variable. Calculation: The covariance of a random variable can be written as, C o v ( X , X ) = μ X X − μ X μ X = μ X 2 − ( μ X ) 2 = σ X 2

4th Edition

ISBN: 9780073401331

Author: William Navidi Prof.

Publisher: McGraw-Hill Education

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Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

Chapter 2.6, Problem 26E

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Prove that Cov(X,X)=σX2.

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Chapter 2.6, Problem 25E

Chapter 2.6, Problem 27E

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Prove that C o v ( X , X ) = σ X 2 .

Solution Summary: The author explains how the covariance of a random variable can be written as, cCov(X,X)=sigma

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Prove that Cov(X,X)=σX2.

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