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Art of Computer Programming, Volume 2, The: Seminumerical Algorithms by Donald E. Knuth

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*3.5. What Is a Random Sequence?

A. Introductory remarks. We have seen in this chapter how to generate sequences

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of real numbers in the range 0 ≤ Un < 1, and we have called them “random” sequences even though they are completely deterministic in character. To justify this terminology, we claimed that the numbers “behave as if they are truly random.” Such a statement may be satisfactory for practical purposes (at the present time), but it sidesteps a very important philosophical and theoretical question: Precisely what do we mean by “random behavior”? A quantitative definition is needed. It is undesirable to talk about concepts that we do not ...

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