Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter VI, The Binomial And The Poisson Distributions, p. 152-153.
“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.
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William Feller 30
Croatian-American mathematician 1906–1970Related quotes

"The Scientific Aspect of Monte Carlo Roulette" (1894)
Note on the Use of this Book, p. xi-xii.
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Fortune's Formula (2005)
Source: V. (1963), Chapter Two, Part II
Context: The rest of the Crew partook of the same lethargy. Raoul wrote for television, keeping carefully in mind, and complaining bitterly about, all the sponsor-fetishes of that industry. Slab painted in sporadic bursts, referring to himself as a Catatonic Expressionist and his work as “the ultimate in non-communication.” Melvin played the guitar and sang liberal folk songs. The pattern would have been familiar—bohemian, creative, arty—except that it was even further removed from reality, Romanticism in its furthest decadence; being only an exhausted impersonation of poverty, rebellion and artistic “soul.” For it was the unhappy fact that most of them worked for a living and obtained the substance of their conversation from the pages of Time magazine and like publications

Give Me Liberty (1936)
Context: Representative government cannot express the will of the mass of the people, because there is no mass of the people; The People is a fiction, like The State. You cannot get a Will of the Mass, even among a dozen persons who all want to go on a picnic. The only human mass with a common will is a mob, and that will is a temporary insanity. In actual fact, the population of a country is a multitude of diverse human beings with an infinite variety of purposes and desires and fluctuating wills.

The World's Religions (1991)
Context: The religions begin by assuring us that if we could see the full picture we would find it more integrated than we would normally suppose. Life gives us no view of the whole. [... ] It is as if life were a great tapestry, which we face from its wrong side. This gives it the appearance of a maze of knots and threads, which for the most part appear chaotic.
From a purely human standpoint the wisdom traditions are the species' most prolonged and serious attempts to infer from the maze on this side of the tapestry the pattern which, on its right side, gives meaning to the whole. As the beauty and harmony of the design derive from the way its parts are related, the design confers on these parts a significance that we, seeing only scraps of the design, do not normally perceive.