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.