**Student Mathematical Library**

Volume: 28;
2005;
150 pp;
Softcover

MSC: Primary 60;

Print ISBN: 978-0-8218-3714-6

Product Code: STML/28

List Price: $34.00

Individual Price: $27.20

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**Electronic ISBN: 978-1-4704-2139-7
Product Code: STML/28.E**

List Price: $34.00

Individual Price: $27.20

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#### Supplemental Materials

# Heads or Tails: An Introduction to Limit Theorems in Probability

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*Emmanuel Lesigne*

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.

#### Table of Contents

# Table of Contents

## Heads or Tails: An Introduction to Limit Theorems in Probability

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Prerequisites and Overview 110 free
- Chapter 1. Modeling a Probabilistic Experiment 312
- Chapter 2. Random Variables 716
- Chapter 3. Independence 1120
- Chapter 4. The Binomial Distribution 1524
- Chapter 5. The Weak Law of Large Numbers 1928
- Chapter 6. The Large Deviations Estimate 2332
- Chapter 7. The Central Limit Theorem 2938
- Chapter 8. The Moderate Deviations Estimate 4554
- Chapter 9. The Local Limit Theorem 5362
- Chapter 10. The Arcsine Law 5968
- Chapter 11. The Strong Law of Large Numbers 7786
- Chapter 12. The Law of the Iterated Logarithm 97106
- Chapter 13. Recurrence of Random Walks 109118
- Chapter 14. Epilogue 131140
- Biographies 137146
- Bibliography 147156
- Index 149158
- Back Cover Back Cover1162

#### Readership

Undergraduates and beginning graduate students interested in mathematical probability.

#### Reviews

This is a delightful little book ... the author converys an impressive and well-written account of central ideas of limit theorems in probability ... It is refreshing to have a book that starts with such a simple experiment with two outcomes and takes us as far as it does into the world of probability theory.

-- MAA Reviews

The proposal is very attractive. ... (It) is helpful for the probability community to have access to this book, which contains a unified and elementary presentation of limit theorems...

-- Zentralblatt Math