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]
^"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
^Inevitable Randomness in Discrete Mathematics by József Beck 2009 ISBN 0-8218-4756-2 page 44
^Algorithms: main ideas and applications by Vladimir Andreevich Uspenskiĭ, Alekseĭ, Lʹvovich Semenov 1993 Springer ISBN 0-7923-2210-X page 166
concept of a randomsequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables...
Intuitively, an algorithmically randomsequence (or randomsequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free...
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably...
random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers...
In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation f n = f n − 1 ± f n...
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable...
In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A randomsequence of events, symbols...
difficult to predict and exhibits statistical behavior similar to a truly randomsequence. PRBS generators are used in telecommunication, such as in analog-to-information...
theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence in distribution...
In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely...
Algorithmically randomsequence Quasi-randomsequenceRandom number generation RandomsequenceRandom variable Random variate Random real Richard Durstenfeld...
for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will...
A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal...
randomsequences or random functions. Sometimes a random variable is taken to be automatically valued in the real numbers, with more general random quantities...
process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes...
pass statistical randomness tests: Every CSPRNG should satisfy the next-bit test. That is, given the first k bits of a randomsequence, there is no polynomial-time...
NIST Statistical Test Suite Randomness Statistical randomness Algorithmically randomsequence Seven states of randomness Wald–Wolfowitz runs test Wolfram...
or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often...
randomized designs, the levels of the primary factor are randomly assigned to the experimental units. To randomize is to determine the run sequence of...
is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quasi-random number sequence. They generalize the...
sequences of 6 bases which are synthesised entirely randomly to give a numerous range of sequences that have the potential to anneal at many random points...
\mathbb {R} ^{n},} a randomsequence f : Ω → R ∞ , {\displaystyle \textstyle f:\Omega \to \mathbb {R} ^{\infty },} or a sequence of events ( A 1 , A 2...
deals with random samples. A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent...
used as a basis for deriving pseudo-randomsequences in digital communication systems that employ direct-sequence spread spectrum and frequency-hopping...
under certain assumptions can be interpreted as randomsequences of points, random sets of points or random counting measures. In some mathematical frameworks...
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