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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

3.9★
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?

1. Past research experirence (reinforcenment learning, model explainability). A lot of followups. 2. Bias and variance trade-off in random forest. 3. Linear regression closed-form solution (w/ and w/o L2 regularization).
avatar

Quant Research Intern

Interviewed at Citadel

3.9★
Nov 14, 2021

1. Past research experirence (reinforcenment learning, model explainability). A lot of followups. 2. Bias and variance trade-off in random forest. 3. Linear regression closed-form solution (w/ and w/o L2 regularization).

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