Editing Random sequence (section)

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 variable]]s and many statistical discussions begin with the words "let ''X''<sub>1</sub>,...,''X<sub>n</sub>'' 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".<ref>"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</ref>

[[Probability axioms|Axiomatic probability theory]] ''deliberately'' avoids a definition of a random sequence.<ref>''Inevitable Randomness in Discrete Mathematics'' by József Beck 2009 {{ISBN|0-8218-4756-2}} page 44</ref> 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 [[Nicolas Bourbaki|Bourbaki school]] considered the statement "let us consider a random sequence" an [[abuse of terminology|abuse of language]].<ref>''Algorithms: main ideas and applications'' by Vladimir Andreevich Uspenskiĭ, Alekseĭ, Lʹvovich Semenov 1993 Springer {{ISBN|0-7923-2210-X}} page 166</ref>