Probabilities; Convergence; Error analysis; Pascal's theorem; Laplace's theorem; Bayes' theorem; Probabilités; Théorie des erreurs; Théorème de Pascal; Théorème de Laplace; Théorème de Bayes
Abstract :
[en] The author wants to increase the accuracy of the probability calculations and concentrate the methods and principles in the presentation of the probabilities theory. First, he puts no doubt on the series convergence by means of three demonstrated theorems. Then he resorts to an only process, the Fourier’s and Lejeune-Dirichlet’s theorems, for to equate. Finally, he highlights the dependence of the special cases of the probabilities theory due to Laplace. [fr] L’auteur veut rendre plus rigoureux les calculs des probabilités et concentrer les méthodes et les principes dans l’exposition de la théorie des probabilités à postériori. Il met d’abord hors de doute la convergence des séries à l’aide de trois théorèmes démontrés. Il a ensuite recours à un procédé unique, les théorèmes de Fourier et de Lejeune-Dirichlet, pour la mise en équation. Enfin, il fait ressortir la dépendance des cas spéciaux de la théorie des probabilités à postériori due à Laplace.
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