Uspensky J.V. Introduction to mathematical probability

New York; Toronto; London: McGraw-Hill Book Company, 1965. — 411 p.This book is an outgrowth of lectures on the theory of probability which the author has given at Stanford University for a number of years. At first a short mimeographed text covering only the elementary parts of the subject was used for the guidance of students. As time went on and the scope of the course was gradually enlarged, the necessity arose of putting into the hands of students a more elaborate exposition of the most important parts of the theory of probability. Accordingly, a rather large manuscript was prepared for this purpose. The author did not plan at first to publish it, but students and other persons who had opportunity to peruse the manuscript were so persuasive that publication was finally arranged.1st ed. /file/3461723/Preface.
Introduction.
Computation or probability by direct enumeration of cases.
Theorems of total and compound probability.
Repeated trials.
Probabilities of hypotheses and Bayes’ theorem.
Use or difference equations in solving problems of probability.
Bernoulli’s theorem.
Approximate evaluation of probabilities in Bernoullian case.
Further considerations on games or chance.
Mathematical expectation.
The law or large numbers.
Application of the law or large numbers.
Probabilities in continuum.
The general concept or distribution.
Fundamental limit theorems.
Normal distribution in two dimensions.
Distribution or certain functions or normally distributed variables.