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

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.
This research was supported by the Russian Foundation for Basic Research, grant 02–01–00985, and by the program of the President of Russian Federation for supporting leading scientific schools, grant 00–15–96103.