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Two real-valued RVs, X and Y, have joint PDF 1 p(x, x2) = exp 2TV1-r (x; – 2rx,x2 2(1 - r) where -1

Two real-valued RVs, X and Y, have joint PDF 1 p(x, x2) = exp 2TV1-r (x; – 2rx,x2 2(1 - r) where -1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 44E
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Two real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1 <r< 1. Prove that cach of X and Y is normally distributed with mean 0 and variance 1. Prove that the number r is the correlation coefficient of X and Y.
Transcribed Image Text:Two real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1 <r< 1. Prove that cach of X and Y is normally distributed with mean 0 and variance 1. Prove that the number r is the correlation coefficient of X and Y.
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