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Random Variables and Probability Distributions

$51.99 (C)

Part of Cambridge Tracts in Mathematics

  • Date Published: June 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521604864

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  • 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.

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    Product details

    • Date Published: June 2004
    • format: Paperback
    • isbn: 9780521604864
    • length: 132 pages
    • dimensions: 216 x 140 x 8 mm
    • weight: 0.18kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    H. Cramer, Stockholms Universitet

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