Using the Cauchy Schwarz inequality, show that for any two random variables X and Y (X,Y) 1 Also, (X,Y ) 1 if and only if Y aX b for some constants a, b R ...

Let U which implies X EX ox Then EU EV 0 and VarU VarV 1 Using the CauchySchwarz ...

Using the Cauchy-Schwarz inequality, show that for any two random variables X and Y |(X,Y)| 1.

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Using the Cauchy-Schwarz inequality, show that for any two random variables X and Y |ρ(X,Y)| ≤ 1.

Also, |ρ(X,Y )| = 1 if and only if Y = aX +b for some constants a, b ∈ R.

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Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

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Question Posted: Oct 27, 2023 02:25 AM

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Using the Cauchy-Schwarz inequality, show that for any two random variables X and Y |(X,Y)| 1.

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Introduction To Probability Statistics And Random Processes

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