The paper concerns discrete transformations of finite-valued random variables, i.e. random variables which have a finite number of values, with rational probabilities of values. By a discrete transformation of finite-valued random variables we mean a random variable with finite number of values which are the values of an arbitrary finite-valued function whose variables values are the values of the independent initial random variables. The closure of a set of finite rational probabilistic distributions, i.e. distributions consisting of a finite number of rational probabilities, is the set of finite rational probabilistic distributions for all random variables obtained by discrete transformations of finite-valued random variables whose probabilistic distributions belong to the initial set of probabilistic distributions. In the paper the closures of all finite sets of finite rational probabilistic distributions are described. Moreover, an effective procedure of checking if a given finite rational probabilistic distribution can be obtained by discrete transformations from a given finite set of finite rational probabilistic distributions is proposed.

finite-valued random variables, discrete transformation, closed class

Mathematical problems and theory of numerical methods