Probability Theory

ForewordTranslator's PrefaceAuthor's PrefaceIntroductionI Prehistory of Probability Theory 1 Basic stimuli in the rise of probability theory 2 The role of gambling in the rise of probability theory 3 The first problems 4 Cardano and Tartaglia 5 Elements of probability theory in Galileo's works 6 Basic stages in the development of combinatoricsII The First Stage in the Development of Probability Theory 1 De Mere's legend 2 Letters between Fermat and Pascal 3 Contributions of Huygens to probability theoryIII The Development of Probability Theory to the Middle of the Nineteenth Century 1 James Bernoulli and his treatise "Ars Conjectandi" 2 The development of probability theory in the first half of the eighteenth century 3 Simpson's contributions to probability theory 4 Thomas Bayes and his theorem 5 Euler's and Daniel Bernoulli's contributions 6 G. L. Buffon 7 Opposition from d'Alembert 8 Jean Antoine de Caritat, Marquis de Condorcet 9 Laplace and his contributions to probability theory 10 Distribution of random errors 11 The state of probability theory in Europe prior to the advent of the Russian (St. Petersburg) school 12 Probability theory in Russia prior to the advent of the St. Petersburg school 161IV Probability Theory in the Second Half of the Nineteenth Century 1 Chebyshev—the originator of the Russian school of probability theory 2 Prominent representatives of the St. Petersburg school 3 Probability in physics 4 Bertrand's paradoxes V The Axiomatic Foundations of Probability Theory 1 The need for axiomatization 2 Prerequisites for axiomatization 3 Bernstein's contributions 4 The frequency approach of R. von Mises 5 The beginning of a new stage in the development of probability theory Bibliography Index