A remark on the converse of Laplace's theorem

  title={A remark on the converse of Laplace's theorem},
  author={Mikhail Nikulin},
  journal={Journal of Soviet Mathematics},
  • M. Nikulin
  • Published 1 April 1992
  • Mathematics
  • Journal of Soviet Mathematics
UDC 519.21 1. At the beginning of the 1940's S. N. Bernshtein established that in the case of the binomial distribution the a posteriori distribution of the probability of positive outcome as the number of experiments increases without bound is practically independent of the a priori distribution. Bernshtein proved this fact under the assumption that the binomial distribution satisfies the hypotheses of the central limit theorem (in the present case, the hypotheses of Laplace's theorem). In… 
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