"Problems for solution" with answers at end of each chapter. "References" at end of each chapter except chapters I and III.

Computation of probability by direct enumeration of cases -- Theorems of total and compound probability -- Repeated trials -- Probabilities of hypotheses and Bayes' theorem -- Use of difference equations in solving problems of probability -- Bernoulli's theorem -- Approximate evaluation of probabilities in Bernoullian case -- Further considerations on games of chance -- Mathematical expectation -- The law of large numbers -- Application of the law of large numbers -- Probabilities in continuum -- The general concept of distribution -- Fundamental limit theorems -- Normal distribution in two dimensions. Limit theorem for sums of independent vectors. Origin of normal correlation -- Distribution of certain functions of normally distributed variables -- Appendix I. Euler's summation formula--Stirling's formula--some definite integrals -- Appendix II. Method of moments and its applications -- Appendix III. On a Gaussian problem.