Derive lower bound for equicorrelation rho
Company: Citadel
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
Let X, Y, Z be zero-mean, unit-variance random variables whose pairwise correlations are all equal to ρ. Find the tight lower bound on ρ such that the 3×3 correlation matrix is positive semidefinite. Show your work by analyzing eigenvalues of the equicorrelation matrix. Then generalize: for n variables with common off-diagonal correlation ρ, derive the feasible interval of ρ as a function of n.
Overview: This question evaluates understanding of positive semidefiniteness for equicorrelation matrices, eigenvalue analysis, and parameter constraints in multivariate statistics.
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