Theory of Probability

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This treatise is written on an elementary level; in more difficult cases the final formulas are provided without proof. Nevertheless, it was impossible to leave out integrals and I also had to differentiate an integral with respect to a parameter. I include many examples taken from the history of probability and hope that my subject has thus become lively. I especially quote Karl Pearson's (1978, p. 1) repentant confession: I do feel how wrongful it was to work for so many years at statistics and neglect its history. In spite of a few mistakes, his book deserves serious attention. Thus, in ? 4.1.1 I criticize his opinion about Jakob Bernoulli. I have devoted much attention to the notion of probability which fully conforms to Langevin's statement (1913/1914, p. 3): Dans toutes ces questions [in the kinetic theory] la difficulte principale est, comme nous le verrons, de donner une definition correcte et claire de la probabilite. Note however that correct definition sounds strangely.