Studies in the history of probability and statistics. XXI.

Abstract

SUMMARY This paper is devoted to the early history of the law of large numbers. An outline of the prehistory of this law is given in ? 1. The algebraic part of J. Bernoulli's theorem is presented in a logarithmic form and the lesser known role of N. Bernoulli is described in ? 2. Comments on the derivation of the De Moivre-Laplace limit theorems by De Moivre, in particular, on the inductive character of his work, on the priority of De Moivre as to the continuous uniform distribution, on the unaccomplished possibility of Simpson having arrived at the normal distribution and on the role of Laplace are presentedin ? 3. The historical role of J. Bernoulli's form of the law of large numbers is discussed in ? 4.