Geodesic
Construction of random variables according to probabilities of their binary digits
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 160-163

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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. 
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     author = {B. B. Pokhodzei},
     title = {Construction of random variables according to probabilities of their binary digits},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {160--163},
     publisher = {mathdoc},
     volume = {166},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a17/}
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B. B. Pokhodzei. Construction of random variables according to probabilities of their binary digits. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 160-163. http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a17/