Probability Theory by Yuan Shih Chow

Probability Theory by Yuan Shih Chow

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Summary

limit theorems for martingale arrays, the central limit theorem for the interchangeable and martingale cases, moment convergence in the central limit theorem; complete discussion, including central limit theorem, of the random casting of r balls into n cells;

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Probability Theory by Yuan Shih Chow

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 sub- ject, generally attributed to investigations by the renowned French mathe- 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).
SKU Unavailable
ISBN 13 9780387406077
ISBN 10 0387406077
Title Probability Theory
Author Yuan Shih Chow
Series Springer Texts In Statistics
Condition Unavailable
Binding Type Paperback
Publisher Springer-Verlag New York Inc.
Year published 2003-10-17
Number of pages 489
Cover note Book picture is for illustrative purposes only, actual binding, cover or edition may vary.