William Feller: Probability

“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 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

“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

“In stochastic processes the future is not uniquely determined, but we have at least probability relations enabling us to make predictions.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter XV, Markov Chains, p. 420.

Future

“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

“To every event defined for the original random walk there corresponds an event of equal probability in the dual random walk, and in this way almost every probability relation has its dual.”

William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter III, Fluctuations In Coin Tossing And Random Walks, p. 92.

Way

“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

“When this book was first conceived (more than 25 years ago) few mathematicians outside the Soviet Union recognized probability as a legitimate branch of mathematics.”

William Feller

Preface to the Third Edition, p. vii.
An Introduction To Probability Theory And Its Applications (Third Edition)

Books , Mathematics

“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

“The philosophy of the foundations of probability must be divorced from mathematics and statistics, exactly as the discussion of our intuitive space concept is now divorced from geometry.”

William Feller

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

Mathematics