"Warning. It is usual to read into the law of large numbers things which it definitely does not imply. If Peter and Paul toss a perfect coin 10,000 times, it is customary to expect that Peter will be in the lead roughly half the time. This is not true. In a large number of different coin-tossing games it is reasonable to expect that any fixed moment heads will be in the lead in roughly half of all cases. But it is quiet likely that the player who ends at the winning side has been in the lead for practically the whole duration of the game. Thus, contrary to widespread belief, the time average for any individual game has nothing to do with the ensemble average at any given moment."
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RefugeesMathematicians from the United StatesAcademics from CroatiaMathematicians from CroatiaPeople from Zagreb
Original Language: English
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Chapter VI, The Binomial And The Poisson Distributions, p. 152-153.
https://en.wikiquote.org/wiki/William_Feller
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William Feller
William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory. Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States.
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