Heads or Tails: An Introduction to Limit Theorems in Probability (Student Mathematical Library Series, Volume 28)

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More About This Textbook

Overview

Everyone knows some of the basics of probability, perhaps enough to play cards. Beyond the introductory ideas, there are many wonderful results that are unfamiliar to the layman, but which are well within our grasp to understand and appreciate. Some of the most remarkable results in probability are those that are related to limit theorems—statements about what happens when the trial is repeated many times. The most famous of these is the Law of Large Numbers, which mathematicians, engineers, economists, and many others use every day. In this book, Lesigne has made these limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails. In this way, the analysis becomes much clearer, helping establish the reader's intuition about probability. Moreover, very little generality is lost, as many situations can be modelled from combinations of coin tosses. This book is suitable for anyone who would like to learn more about mathematical probability and has had a one-year undergraduate course in analysis.

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Product Details

  • ISBN-13: 9780821837146
  • Publisher: American Mathematical Society
  • Publication date: 6/2/2005
  • Series: Student Mathematical Library , #28
  • Edition description: New Edition
  • Pages: 150
  • Product dimensions: 5.50 (w) x 8.46 (h) x 0.36 (d)

Table of Contents

Ch. 1 Modeling a probabilistic experiment 3
Ch. 2 Random variables 7
Ch. 3 Independence 11
Ch. 4 The binomial distribution 15
Ch. 5 The weak law of large numbers 19
Ch. 6 The large deviations estimate 23
Ch. 7 The central limit theorem 29
Ch. 8 The moderate deviations estimate 45
Ch. 9 The local limit theorem 53
Ch. 10 The Arcsine law 59
Ch. 11 The strong law of large numbers 77
Ch. 12 The law of the iterated logarithm 97
Ch. 13 Recurrence of random walks 109
Ch. 14 Epilogue 131
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