Theory of Probability

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 difficulté principale est comme nous le verrons de donner une définition correcte et claire de la probabilité. Note however that correct definition sounds strangely.