Random Variables and Probability Distributions

This tract develops the purely mathematical side of the theory of probability.

H. Cramer (Author)

9780521604864, Cambridge University Press

Paperback, published 3 June 2004

132 pages
21.6 x 14 x 0.8 cm, 0.18 kg

This tract develops the purely mathematical side of the theory of probability, without reference to any applications. When originally published, it was one of the earliest works in the field built on the axiomatic foundations introduced by A. Kolmogoroff in his book Grundbegriffe der Wahrscheinlichkeitsrechnung, thus treating the subject as a branch of the theory of completely additive set functions. The author restricts himself to a consideration of probability distributions in spaces of a finite number of dimensions, and to problems connected with the Central Limit Theorem and some of its generalizations and modifications. In this edition the chapter on Liapounoff's theorem has been partly rewritten, and now includes a proof of the important inequality due to Berry and Esseen. The terminology has been modernized, and several minor changes have been made.

Preface to the first edition
Preface to the second edition
Preface to the third edition
Abbreviations
Part I. Principles: 1. Introductory remarks
2. Axioms and preliminary theorems
Part II. Distributions in R1: 3. General properties
4. Characteristic functions
5. Addition of independent variables
6. The normal distribution and the central limit theorem
7. Error estimation
8. A class of stochastic processes
Part III. Distributions in R2: 9. General properties
10. The normal distribution and the central limit theorem
Bibliography.

Subject Areas: Probability & statistics [PBT]