7. Probability and Statistics Soviet Essays - Sheynin, Oscar

Some groups of mathematicians in Moscow, Leningrad and other cities are enthusiasticallyhelping scientists of other specialities in solving practical problems in biology, geology, etcby statistical methods. But I have already mentioned that this work is somewhat casual,uncoordinated and sometimes amateurish. At a future conference, our branch ought to payattention to the problem of organizing such work more rationally and wider.Notes1. {This is a paraphrase rather than a quotation from Krylov’s Foreword to Chebyshev’slectures on probability theory published in 1936; translation: Berlin, 2004.}2. {See Bolshev, L.N., Smirnov, N.V. (1968), ) (Tables of Mathematical Statistics). M.}15. B.V. Gnedenko. Theory of Probability and Mathematical Statistics. Introduction. In (History of National Mathematics), vol. 4/2.Editor, I.Z. Stokalo. Kiev, 1970, pp. 7 – 13 …Foreword by TranslatorThe following is a translation of the author’s Introduction to the chapter on probabilityand statistics from a monograph on Soviet mathematics during 1917 – 1967. The mainbody of that chapter written by other authors was devoted to limit theorems and the theoryof random processes. Concerning Lobachevsky whom Gnedenko mentioned see my Note3 to Kolmogorov’s paper of 1947 translated in this book.[1] In Russia, the first investigations pertaining to probability theory date back to thebeginning of the 19 th century when Lobachevsky, Ostrogradsky and Buniakovsky, ondifferent occasions, had to solve a number of particular problems. Lobachevsky attemptedto check by observations the geometric system that exercised dominion over the universe.Ostrogradsky examined some applied issues including acceptance inspection of goodsdelivered by providers. Buniakovsky also issued from the need to solve practical problemsand he published a fundamental treatise (1846). This initial acquaintance with the theory ofprobability was a necessary and important period in developing an interest in this branchof mathematics in Russia.The formulation and solution of general problems in the theory, and its initial formationas a vast mathematical science, characterized by a specific formulation of issues playingthe main part in the entire domain of natural sciences, are connected with Chebyshev,Liapunov and Markov. By proving the law of large numbers {in a general setting}Chebyshev not only opened a general and important scientific regularity; he also providedan exceptionally simple and powerful method for the theory of probability and the entirefield of mathematics. Later Markov perceived that the Chebyshev method allowed toestablish {still} wider conditions for the applicability of the law of large numbers. Theestimation of the probability, that the deviations of arithmetic means of independentrandom variables from the {appropriate} constants will not exceed the boundaries givenbeforehand, was a natural extension of investigating the conditions for the means toapproximate a sequence of these constants.By Chebyshev’s time the classical findings of De Moivre and Laplace concerning theBernoulli pattern were only generalized to sequences of independent trials with a variableprobability of success. However, the theory of observational errors insistently demandedwider generalizations 1 . Laplace and Bessel surmised that, if the observational error was asum of a very large number of errors, each of them being small as compared with the sum