Probability and Statistics: The Science of Uncertainty

Table of Contents......Page 8
Acknowledgments......Page 11
Introduction......Page 12
Part One: What is Probability?......Page 16
1. The Idea of Randomness......Page 18
Randomness before the Theory of Probability......Page 21
Early Difficulties in Developing a Theory of Randomness......Page 26
Randomness and Religion Today in Burkina Faso......Page 27
2. The Nature of Chance......Page 30
Cardano\'s Mistake......Page 32
Cardano on Luck and Math......Page 33
Galileo Galilei......Page 36
Peirre de Fermat and Blaise Pascal......Page 39
The Division of Stakes, an Alternative Interpretation......Page 43
Christian Huygens......Page 45
Jacob Bernoulli......Page 46
Abraham de Moivre......Page 52
De Moivre on Math and Luck......Page 55
The Bell Curve......Page 57
3. Surprising Insights into Probability and Its Uses......Page 60
Thomas Bayes and Inverse Probability......Page 61
Buffon and the Needle Problem......Page 65
Daniel Bernoulli and Smallpox......Page 68
Jean le Rond d\'Alembert and the Evaluation of Risk......Page 72
Leonhard Euler and Lotteries......Page 75
4. Randomness in a Deterministic Universe......Page 79
Simeon-Denis Poisson......Page 86
The Poisson Distribution......Page 87
5. Random Processes......Page 90
James Clerk Maxwell......Page 93
Brownian Motion Revisited......Page 96
Markov Processes......Page 98
A Markov Chain......Page 100
6. Probability as a Mathematical Discipline......Page 102
Theory and Practice......Page 109
Nuclear Reactor Safety......Page 116
Markov Chains and Information Theory......Page 118
Smallpox in Modern Historical Times......Page 120
Part Two: Statistics......Page 126
Introduction: The Age of Information......Page 128
8. The Beginnings of Statistics......Page 130
The Beginnings of Statistics......Page 132
Edmund Halley......Page 135
Breslau Table for Number and Infinity......Page 139
Insurance......Page 141
9. Data Analysis and the Problem of Precision......Page 145
The Misuse of Statistics......Page 149
10. The Birth of Modern Statistics......Page 151
Karl Pearson......Page 152
R.A. Fisher......Page 157
11. The Theory of Sampling......Page 165
The Problem......Page 166
Walter Shewhart and Statistical Quality Control......Page 169
William Edwards Deming......Page 174
The Birth of Epidemiology......Page 180
The U.S. Census......Page 186
Political Polling......Page 192
Chronology......Page 198
Glossary......Page 215
Further Reading......Page 218
Index......Page 230