Statistics Graduate Level Quiz
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ADVANCED TOPICS IN GRADUATE STATISTICS
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Three standardized random variables have pairwise correlations Corr⁡(X,Y)=Corr⁡(Y,Z)=ρ\operatorname{Corr}(X,Y)=\operatorname{Corr}(Y,Z)=\rho and Corr⁡(X,Z)=0\operatorname{Corr}(X,Z)=0, where ρ≥0\rho\ge 0. What is the largest value of ρ\rho for which these correlations can define a valid correlation matrix?
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