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There are three random variables, $X,Y,Z$. The three correlations between the three variables are the same. That is, $$\rho = \Corr(X,Y) = \Corr(Y,Z) = \Corr (Z,X)$$ What is the tightest bound you can give for $\rho$? How about the general case for $n$ random variables?
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Quant Researcher

Interviewed at Citadel

4★
Apr 10, 2024

There are three random variables, $X,Y,Z$. The three correlations between the three variables are the same. That is, $$\rho = \Corr(X,Y) = \Corr(Y,Z) = \Corr (Z,X)$$ What is the tightest bound you can give for $\rho$? How about the general case for $n$ random variables?

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