Three random variables X₁, X₂, X3 have equal variances o2 and coefficient of correlation between X₁ and X₂ of p and between X and X3 and between X and X3 of zero. Find the correlation between Y and Z, where YX₁ + X2, and Z = X₂ + X3 A. 1+P B. √I+P C. 20² (1+p) D. 2√√1+P E. IFP

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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Three random variables X₁, X2, X3 have equal variances o2 and coefficient of correlation between
X₁ and X₂ of p and between X₁ and X3 and between X and X3 of zero. Find the correlation
between Y and Z, where YX₁ + X₂, and Z = X₂ + X3
A. 1+p B. √I+P
C. 20² (1+p)
D. 21+P
Transcribed Image Text:Three random variables X₁, X2, X3 have equal variances o2 and coefficient of correlation between X₁ and X₂ of p and between X₁ and X3 and between X and X3 of zero. Find the correlation between Y and Z, where YX₁ + X₂, and Z = X₂ + X3 A. 1+p B. √I+P C. 20² (1+p) D. 21+P
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