William Feller: Theory

“The theory of independent experiments is the analytically simplest and most advanced part of probability theory.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter V, Conditional Probability, Stochastic Independence, p. 132.

Parting

“The notion of conditional probability is a basic tool of probability theory, and it is unfortunate that its great simplicity is somewhat obscured by a singularly clumsy terminology.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter V, Conditional Probability, Stochastic Independence, p. 114.

“Historically, the original purpose of the theory of probability was to describe the exceedingly narrow domain of experience connected with games of chance, and the main effort was directed to the calculation of certain probabilities.”

William Feller

Introduction, The Nature of Probability Theory, p. 3.
An Introduction To Probability Theory And Its Applications (Third Edition)

Game , Effort , Chance

“The manner in which mathematical theories are applied does not depend on preconceived ideas; it is a purposeful technique depending on, and changing with, experience.”

William Feller

Introduction, The Nature of Probability Theory, p. 2 - 3.
An Introduction To Probability Theory And Its Applications (Third Edition)

Mathematics , Idea , Change , Dependency

“The classical theory of probability was devoted mainly to a study of the gamble's gain, which is again a random variable; in fact, every random variable can be interpreted as the gain of a real or imaginary gambler in a suitable game.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter IX, Random Variables; Expectation, p. 212.

Game , Study

“Only yesterday the practical things of today were decried as impractical, and the theories which will be practical tomorrow will always be branded as valueless games by the practical man of today.”

William Feller

Introduction, The Nature of Probability Theory, p. 6.
An Introduction To Probability Theory And Its Applications (Third Edition)

Game

“Infinite product spaces are the natural habitat of probability theory.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter V, Conditional Probability, Stochastic Independence, p. 130

Nature

“The painful experience of many gamblers has taught us the lesson that no system of betting is successful in improving the gambler's chances. If the theory of probability is true to life, this experience must correspond to a provable statement.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter VIII, Unlimited Sequences Of Bernoulli Trials, p. 198.

Life , Pain , Chance , Success

“The results concerning fluctuations in coin tossing show the widely held beliefs about the law of large numbers are fallacious. They were so amazing and so at variance with common intuition that even sophisticated colleagues doubted that coins actually misbehave as theory predicts.”

William Feller

Note on the Use of this Book, p. xi-xii.
An Introduction To Probability Theory And Its Applications (Third Edition)

Law

“The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has nothing to do with imperfections of physical coins; it endows nature with memory, or, in our terminology, it denies the stochastic independence of successive trials. Marbe's theory cannot be refuted by logic but is rejected because of empirical support.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter VI, The Binomial And The Poisson Distributions, p. 147.

Support , Nature , Memory , Success

“This faulty intuition as well as many modern applications of probability theory are under the strong influence of traditional misconceptions concerning the meaning of the law of large numbers and of a popular mystique concerning a so-called law of averages.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter X, Law Of large Numbers, p. 250.

Law , Strong