CHAPTER 4
Discrete Probability Theory
My favorite reference book in probability is An Introduction to Probability Theory and Its Applications by William Feller [Feller 1957].
Another more recent excellent choice is Grimmett and Stirzaker’s Probability and Random Processes [1992].
4.1 THE ORIGINS OF PROBABILITY THEORY
Probability theory formalizes the notion of randomness, just as Euclid axiomatized geometry by abstracting the intrinsic properties of lines and points and their interrelations. Fermat and Pascal introduced probabilistic reasoning more than 300 years ago to explain the outcomes in games of chance.
Jacob Bernoulli (1654–1705) was a member of a large family of scientists and mathematicians. His book Ars Conjectandi published in 1713 proved the law of large numbers, certainly the most fundamental result in probability. Abraham de Moivre (1667–1754) published a proof in 1733 of the central limit theorem, the second cornerstone of probability. De Moivre’s 1718 book Doctrine of Chance used probability theory to explain the nature of games of chance to gamblers.
Still, the development of probability theory as an independent mathematical discipline begsn in 1812 in Théorie Analytique des Probablités by Pierre Simon Laplace (1749–1817).
Questions in statistical mechanics motivated the subsequent development of the subject; the two major publications were the following:
1933 Andrey Nikolaevich Kolmogorov (1903–1987), Grundbegriffe des Warcheinlichkeitrechnung (Foundations of ...
