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.