Construction of random variables according to the probabilities of their binary digits

One states special properties of binary expansions of random variables, having a truncated geometric (discrete uniform) and exponential (uniform) distributions, which simplify in an essential manner the construction of random variables according to the probabilities of their binary digits.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 166, pp. 160–163, 1988.