William Feller Quotes

William "Vilim" Feller , born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory. Wikipedia  

✵ 7. July 1906 – 14. January 1970
William Feller: 30   quotes 0   likes

Famous William Feller Quotes

“Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction.”

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter XV, Markov Chains, p. 397.

“The fact that the mean recurrence time is infinite implies that the chance fluctuations in an individual prolonged coin-tossing game are far removed from the familiar pattern governed by the normal distribution.”

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter XIII, Recurrent Events. Renewal Theory. p. 314.

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

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

“Note the situation is different when the player is permitted to vary his stakes. In this case there exist advantageous strategies, and the game depends on the strategy.”

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter VIII, Unlimited Sequences Of Bernoulli Trials, p. 200

“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.”

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

William Feller Quotes about the game

“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.”

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

“It must be understood that a fair game may be distinctly unfavorable to the player.”

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter X, Law Of large Numbers, p. 249.
Context: Much harm was done by the misleading suggestive power of this name. It must be understood that a fair game may be distinctly unfavorable to the player.

William Feller Quotes

“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.”

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

“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.”

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

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

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

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

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

“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.”

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

“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.”

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

“When a coin is tossed, it does not necessarily fall heads or tails; it can roll away or stand on its edge.”

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter I, The Sample Space, p. 7

“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.”

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

“It is a common fallacy to believe that the law of large numbers acts as a force endowed with memory seeking to return to the original state, and many wrong conclusions have been drawn from this assumption.”

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter V, Conditional Probability, Stochastic Independence, p. 136.

“three repairman per twenty machines are much more economical than one repairman per six machines.”

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter XVII, The Simplest Time Dependent Stochastic Processes, p. 466.

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