On multivalued transformations of finite sets of binary distributions with rational probabilities

Abstract

We study discrete transformations of independent random variables which take a finite number of values with rational probabilities (by a discrete transformation of random variables is meant a random variable whose value is a function of the values of original random variables). We find explicitly all possible probability distributions of random variables which can be obtained by discrete transformations of random variables with distributions belonging to an arbitrary finite set of binary rational distributions.