Springer Texts in Statistics

Probability Theory

Independence, Interchangeability, Martingales

Authors: Chow, Yuan S., Teicher, Henry

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About this Textbook

Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the subĀ­ ject, generally attributed to investigations by the renowned French matheĀ­ matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the Italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933).

Table of contents (12 chapters)

  • Classes of Sets, Measures, and Probability Spaces

    Chow, Yuan Shih (et al.)

    Pages 1-29

  • Binomial Random Variables

    Chow, Yuan Shih (et al.)

    Pages 30-53

  • Independence

    Chow, Yuan Shih (et al.)

    Pages 54-83

  • Integration in a Probability Space

    Chow, Yuan Shih (et al.)

    Pages 84-112

  • Sums of Independent Random Variables

    Chow, Yuan Shih (et al.)

    Pages 113-158

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4684-0504-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-1-4684-0506-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Probability Theory
Book Subtitle
Independence, Interchangeability, Martingales
Authors
Series Title
Springer Texts in Statistics
Copyright
1988
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4684-0504-0
DOI
10.1007/978-1-4684-0504-0
Softcover ISBN
978-1-4684-0506-4
Series ISSN
1431-875X
Edition Number
2
Number of Pages
XVIII, 467
Additional Information
Originally published as a monograph
Topics