What Intraclass Covariance Structures Can Symmetric Bernoulli Random Variables Have?

Abstract

The covariance matrix of random variables $$X_{1},\dots,X_{n}$$ is said to have an intraclass covariance structure if the variances of all the $$X_{i}$$ ’s are the same and all the pairwise covariances of the $$X_{i}$$ ’s are the same. We provide a possibly surprising characterization of such covariance matrices in the case when the $$X_{i}$$ ’s are symmetric Bernoulli random variables.