What Intraclass Covariance Structures Can Symmetric Bernoulli Random Variables Have?

Abstract: The covariance matrix of random variables

X_{1}, d o t s, 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.

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