Probability and Statistics in the 18th Century

This, now slightly revised text, is intended for a broader circle of readers. It appeared in Italian, although with suppressed references, as Lo sviluppo della teoria della probabilità e della statistica in Storia della Scienza, t. 1. Introduction The theory of probability can be traced back to 1654 when Pascal and Fermat, in solving the problem of points (of sharing the stakes in an uncompleted series of games of chance), indirectly introduced the notion of expected gain (of the expectation of a random variable). In 1657, Huygens published the first treatise on probability. There, he applied the new notion (although not its present term) for studying games of chance. His materials of 1669, which remained unknown during his lifetime, included solutions of stochastic problems in mortality. Later, in 1690, following Descartes, he stated that natural sciences only provided morally certain (highly probable) deductions. Moral certainty and the application of statistical probability were discussed in in philosophical literature (Arnauld & Nicole 1662) which influenced Jakob Bernoulli, the future cofounder of probability theory (§2). Petty and Graunt, in the mid-17