Barbour, A. D.; Chen, L. H. Y. - In: Statistics & Probability Letters 14 (1992) 3, pp. 235-241
It is shown that the distribution of the number of ones in the binary expansion of an integer chosen uniformly at random from the set 0, 1,..., n - 1 can be approximated in total variation by a mixture of two neighbouring binomial distributions, with error of order (log n)-1. The proof uses...