What Intraclass Covariance Structures Can Symmetric Bernoulli Random Variables Have?

10/04/2022

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by   Iosif Pinelis, et al.

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The covariance matrix of random variables X_1,…,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.