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Random sequence

The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let X1,...,Xn be independent random variables...". Yet as D. H. Lehmer stated in 1951: "A random sequence is a vague notion... in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians".[1]

Axiomatic probability theory deliberately avoids a definition of a random sequence.[2] Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness. The Bourbaki school considered the statement "let us consider a random sequence" an abuse of language.[3]

  1. ^ "What is meant by the word Random" in Mathematics and common sense by Philip J. Davis 2006 ISBN 1-56881-270-1 pages 180-182
  2. ^ Inevitable Randomness in Discrete Mathematics by József Beck 2009 ISBN 0-8218-4756-2 page 44
  3. ^ Algorithms: main ideas and applications by Vladimir Andreevich Uspenskiĭ, Alekseĭ, Lʹvovich Semenov 1993 Springer ISBN 0-7923-2210-X page 166

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