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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

8. PoissonPoisson introduced the concepts **of** random variable and distributionfunction. He contributed to limit theorems and brought into use the law**of** large numbers proving it for the case **of** Poisson trials, studiedcriminal statistics and systematically determined the significance **of**empirical discrepancies which proved essential for the development **of**statistics and stressed the difference between subjective and objectiveprobabilities.Key words: law **of** large numbers, criminal statistics, medicalstatistics, null hypothesis8.1. Probability and **Statistics**8.1.1. General Statements. Libri Carruci et al (1834, p. 535)advocated the need for basing statistics on the theory **of** probability:The most sublime problems **of** the arithmétique sociale can only beresolved with the help **of** the theory **of** probability.For their part, Double et al (1835, p. 174) noted its connection withtreating mass phenomena:**Statistics** carried into effect always is, after all, the functioningmechanism **of** the calculus **of** probability, necessarily concerning infinite [?]masses, an unrestricted number **of** facts; and (p. 176) [with respect to theapplicability **of** mathematics] the state **of** the medical sciences is not worsethan, not different from the situation with all the physical and naturalsciences, jurisprudence, moral and political sciences etc.Social arithmetic denoted demography, medical statistics and actuarialscience. In both cases Poisson was co-author.He (1837a, pp. 1 and 36) remarked that in the 18 th century,probability became a main branch **of** mathematics with respect both tothe number and utility **of** its applications and the kind **of** analysiswhich it engendered. And, too categorically: No other part **of**mathematics is capable **of** more or more immediately usefulapplications.On pp. 35 – 36 Poisson defined the aims **of** the theory **of** probabilityas determining the cause for believing that a thing is true, and forcomparing those causes for widely differing problems. He added thatThese principles should be regarded as a necessary supplement tologic. The connection **of** probability with logic originated with Leibnizand Lambert and was developed in the 19 th century by Boole, Jevonsand Venn.Poisson (1837a) consistently demanded to check the significance **of**empirical discrepancies, for example between results **of** different series**of** observations; along with Bienaymé, he was therefore the Godfather**of** the Continental direction **of** statistics (§ 14.1). True, his approachwas restricted (§ 8.5).73