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On generating sets of binary random variables with specified first- and second- moments

We study the problem of generating sets of binary random variables with specified means and pairwise correlations (i.e., specified individual- and pairwise-joint- probabilities). We propose a low-complexity algorithm for generating such correlated random variables, that involves first generating a set of mutually independent “source” binary random variables and then constructing the desired random variables by randomly selecting from and probabilistically copying or anticopying the source variables. We show that the parameters of this data-generation algorithm can be easily designed to achieve the desired statistics, under broad conditions.