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Sequence of random variables
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
Random_sequence
Binary sequence
Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free
Algorithmically random sequence
Algorithmically_random_sequence
Apparent lack of pattern or predictability in events
In common usage, randomness is the apparent or actual lack of definite patterns or predictability in information. A random sequence of events, symbols
Randomness
Algorithm that generates an approximation of a random number sequence
random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers
Pseudorandom_number_generator
Type of mathematical sequence
values of a low-discrepancy sequence are neither random nor pseudorandom, but such sequences share some properties of random variables and in certain applications
Low-discrepancy_sequence
Creating sequence of numbers that cannot be predicted
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that
Random_number_generation
Appearing random but actually being generated by a deterministic, causal process
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable
Pseudorandomness
Randomized mathematical sequence based upon the Fibonacci sequence
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
Random_Fibonacci_sequence
Seemingly random, difficult to predict bit stream created by a deterministic algorithm
difficult to predict and exhibits statistical behavior similar to a truly random sequence. PRBS generators are used in telecommunication, such as in analog-to-information
Pseudorandom_binary_sequence
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence in distribution
Convergence of random variables
Convergence_of_random_variables
Quality of a numerical sequence of having no recognizable patterns
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
Statistical_randomness
Number generated by a random process
Algorithmically random sequence Quasi-random sequence Random number generation Non-uniform random number generation Random real Random sequence Random variable
Random_number
Software testing technique that tests programs with random inputs
probability of failure is less than 1/100. Random input sequence generation (i.e. a sequence of method calls) Random sequence of data inputs (sometimes called stochastic
Random_testing
Data evaluation test
NIST Statistical Test Suite Randomness Statistical randomness Algorithmically random sequence Seven states of randomness Wald–Wolfowitz runs test Wolfram
Randomness_test
Variable representing a random phenomenon
random sequences or random functions. Sometimes a random variable is taken to be automatically valued in the real numbers, with more general random quantities
Random_variable
Counterintuitive result in probability
monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. Variants of the theorem include multiple and
Infinite_monkey_theorem
Finite or infinite ordered list of elements
Constant-recursive sequence Geometric progression Harmonic progression Holonomic sequence Regular sequence Pseudorandom binary sequence Random sequence Related concepts
Sequence
Pseudo-random signal with characteristics similar to noise
for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will
Pseudorandom_noise
Internet slang
mash or keyboard smash) is internet slang for the typing out of a random sequence of letters on a computer keyboard or touchscreen, often to express
Keysmash
Sequence where any order is equally likely
A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a
Random_permutation
Type of shift register in computing
function can produce a sequence of bits that appears random and has a very long cycle. Applications of LFSRs include generating pseudo-random numbers, pseudo-noise
Linear-feedback shift register
Linear-feedback_shift_register
Algorithm for generating pseudo-randomized numbers
congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation
Linear_congruential_generator
Numerical integration process
some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences) to achieve variance reduction. This is
Quasi-Monte_Carlo_method
Collection of random variables
some subset of them, then the stochastic process can also be called a random sequence. If the state space is the integers or natural numbers, then the stochastic
Stochastic_process
Value used to initialize a pseudo-random number generator
will produce the same sequence of numbers. For a seed to be used in a pseudorandom number generator, it does not need to be random. Because of the nature
Random_seed
Type of pseudorandom binary sequence
used as a basis for deriving pseudo-random sequences in digital communication systems that employ direct-sequence spread spectrum and frequency-hopping
Maximum_length_sequence
explanation for the origin of eukaryotic introns. It suggests that random primordial DNA sequences would only permit short (< 600bp) open reading frames (ORFs)
Split_gene_theory
Random process of binary (boolean) random variables
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
Bernoulli_process
Halting probability of a random computer program
enumerated. A real number is random if the binary sequence representing the real number is an algorithmically random sequence. Calude, Hertling, Khoussainov
Chaitin's_constant
Swedish logician, philosopher, and mathematical statistician
test for randomness in order to define a random sequence as one that passed all tests for randomness; however, the precise notion of a randomness test was
Per_Martin-Löf
Type of functions designed for being unsolvable by root-finding algorithms
pass statistical randomness tests: Every CSPRNG should satisfy the next-bit test. That is, given the first k bits of a random sequence, there is no polynomial-time
Cryptographically secure pseudorandom number generator
Cryptographically_secure_pseudorandom_number_generator
Concept in statistics
In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely
Exchangeable_random_variables
Cycle through all length-k sequences
The Logic of Scientific Discovery (1934), calling them "shortest random-like sequences". Taking A = {0, 1}, there are two distinct B(2, 3): 00010111 and
De_Bruijn_sequence
Stream cipher
pseudo-random number generator with a 32-bit internal state. Several attacks on RC4 are able to distinguish its output from a random sequence. As a result
RC4
Type of probability space
\mathbb {R} ^{n},} a random sequence f : Ω → R ∞ , {\displaystyle \textstyle f:\Omega \to \mathbb {R} ^{\infty },} or a sequence of events ( A 1 , A 2
Standard_probability_space
Observed value of a random variable
from a pseudo-random sequence. Errors and residuals Outcome (probability) Random variate Raw data Deviation (statistics) Raw score Random number generation
Realization_(probability)
Mathematical notation used in probability and statistics
under certain assumptions can be interpreted as random sequences of points, random sets of points or random counting measures. In some mathematical frameworks
Point_process_notation
a gambling system is a concept in probability. It states that in a random sequence, the methodical selection of subsequences does not change the probability
Impossibility of a gambling system
Impossibility_of_a_gambling_system
Algorithm for shuffling a finite sequence
struck out. The sequence of numbers written down in step 3 is now a random permutation of the original numbers. Provided that the random numbers picked
Fisher–Yates_shuffle
Random variable with multiple component dimensions
of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc. Formally, a multivariate random variable is
Multivariate_random_variable
Type of numeric sequence used in statistics
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
Halton_sequence
Type of sequence in numerical analysis
Sobol' sequences (also called LPτ sequences or (t, s) sequences in base 2) are a type of quasi-random low-discrepancy sequence. They were first introduced
Sobol_sequence
Random sequence whose joint probability distribution is invariant over time
processes, a stationary sequence is a random sequence whose joint probability distribution is invariant over time. If a random sequence X j is stationary then
Stationary_sequence
American biochemist
the Szostak lab, Bartel isolated the first ribozymes directly from random sequence, using in vitro evolution (among these, the Class I ligase). After
David_Bartel
randomized designs, the levels of the primary factor are randomly assigned to the experimental units. To randomize is to determine the run sequence of
Completely_randomized_design
Method for assessing quantum computer hardware capabilities
average error rates by implementing long sequences of randomly sampled quantum gate operations. Randomized benchmarking is the industry-standard protocol
Randomized_benchmarking
Tendency to perceive connections between unrelated things
is a type of cognitive bias in which a person sees a pattern in a random sequence of numbers or events. Many theories have been disproved as a result
Apophenia
Theorem from probability theory
theorem (CLT) to hold for a sequence of independent random variables. Unlike the classical CLT, which requires that the random variables in question have
Lindeberg's_condition
1984 dramatic TV game-show success
rapidly illuminated in a seemingly random sequence until a contestant pressed their button to stop the lights. The sequence was originally limited to only
Press_Your_Luck_scandal
Cryptographic device
hardware random number generator (HRNG), true random number generator (TRNG), non-deterministic random bit generator (NRBG), or physical random number generator
Hardware random number generator
Hardware_random_number_generator
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
Random_hexamer
Concept in probability and statistics
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
Independent and identically distributed random variables
Independent_and_identically_distributed_random_variables
Branch of probability theory
have finite expectation. A renewal-reward process additionally has a random sequence of rewards incurred at each holding time, which are IID but need not
Renewal_theory
Telecommunication device that obscures signals
removes unwanted sequences. A scrambler (or randomizer) can be either: An algorithm that converts an input string into a seemingly random output string of
Scrambler
Channel access method used by various radio communication technologies
"pseudo-noise" sequences called spreading sequences are used in asynchronous CDMA systems. A spreading sequence is a binary sequence that appears random but can
Code-division_multiple_access
American biochemist
developed the first “random selection” method for selecting DNA target sites (and other genetic elements) from random-sequence oligonucleotides. He showed
Kevin_Struhl
Computer security exploit technique
of the fact that the instruction set is very "dense", that is, any random sequence of bytes is likely to be interpretable as some valid set of x86 instructions
Return-oriented_programming
Elementary cellular automaton
obtained by the rule 30 CA may be due to the fact that we considered N random sequences generated in parallel, rather than the single one considered by Wolfram
Rule_30
Conditional independence of exchangeable observations
(i.i.d.) Bernoulli random variables. A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any
De_Finetti's_theorem
Color perception test
or tracing of the numbers by the subject. The test is best given in random sequence, if possible, to reduce the effectiveness of prior memorization of
Ishihara_test
Mathematical theorem
LIL to random walks satisfying milder conditions. A survey up to 1986. Vovk (1987) derived a version of LIL valid for a single chaotic sequence (Kolmogorov
Law_of_the_iterated_logarithm
Election result probability theorem
{p+1-q}{p+1}}} . Barton, D. E.; Mallows, C. L. (1965). "Some Aspects of the Random Sequence". Ann. Math. Statist. 36: 236–260. doi:10.1214/aoms/1177700286. Feller
Bertrand's_ballot_theorem
Encryption technique
the Signal Corps) recognized that the character sequence on the key tape could be completely random and that, if so, cryptanalysis would be more difficult
One-time_pad
Natural number
(ed.). "Sequence A094133 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A094133
17_(number)
Subfield of information theory and computer science
completely random letters, despite the fact that the encyclopedia is much more useful. This is because to reconstruct the entire sequence of random letters
Algorithmic information theory
Algorithmic_information_theory
Class of statistical modeling methods
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured
Conditional_random_field
Process of making something random
sample data to the broader population. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose
Randomization
Computer science professor
algorithmic randomness. He co-authored a paper demonstrating that a recursively enumerable real number is an algorithmically random sequence if and only
Yongge_Wang
2021 Indian film
platforms". A critic from The News Minute wrote that Meow is just a random sequence of events in somebody's life that you get to watch, but you don't really
Meow_(2021_film)
Method used for sequencing random DNA strands
sequence. In shotgun sequencing, DNA is broken up randomly into numerous small segments, which are sequenced using the chain termination method to obtain reads
Shotgun_sequencing
System in which no randomness is involved in determining its future states
algorithm, that is designed to produce sequences of numbers that behave as random sequences. A hardware random number generator, however, may be non-deterministic
Deterministic_system
Form of divination
diviner then casts the dice, resulting in a random sequence of numbers. The diviner interprets this sequence according to certain rules, usually related
Astragalomancy
Uses of an apparent lack of pattern or predictability in events
Randomness has multiple uses in science, art, statistics, cryptography, gaming, gambling, and other fields. For example, random assignment in randomized
Applications_of_randomness
Memory sports player
Memory Tests", being tested on samples from the first 100,000 digits. A random sequence of nine digits were read out and Jonas recalled the nine digits preceding
Jonas_von_Essen
Form of scientific experiment
receives (or does not receive) an intervention in a random sequence. Stepped-wedge trial - " involves random and sequential crossover of clusters (of subjects)
Randomized_controlled_trial
Mathematical problem involving optimal stopping theory
trickiest exchangeable random variable sequence. Bob's strategy is formalizable as a stopping rule τ {\displaystyle \tau } for the sequence X 1 , X 2 , . .
Secretary_problem
Evolutionary science thought experiment
selection of each letter in a sequence of 28 characters will be random. The number of possible combinations in this random sequence is 2728, or about 1040,
Weasel_program
Measure of algorithmic complexity
one Kolmogorov random string of each length. This definition can be extended to define a notion of randomness for infinite sequences from a finite alphabet
Kolmogorov_complexity
Tree-based ensemble machine learning methods
Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that works by creating a multitude
Random_forest
1999 book by John Julius Norwich
chronological order, while Shakespeare composed them in a much more random sequence. Norwich's book covers the history relating to the following plays:
Shakespeare's_Kings
Cryptographical test for pseudo-randomness
pseudo-random sequences. A sequence of words passes Yao's test if an attacker with reasonable computational power cannot distinguish it from a sequence generated
Yao's_test
Submarine communication
correction code using 64 symbols, each represented by a very long pseudo-random sequence. The entire transmission was then encrypted. The advantages of such
Communication_with_submarines
Content of the World Wide Web that is not indexed by search engines
common web browsers. Using this application, deep web links appear as a random sequence of letters followed by the .onion top-level domain. Internet portal
Deep_web
Machine for shuffling playing cards
device did not distribute cards to players but was just displaying a random sequence of cards. However, it used a shuffling mechanism that relied upon a
Shuffling_machine
Probabilistic problem-solving algorithm
measures of the random states of the MCMC sampler.[citation needed] In other problems, the objective is generating draws from a sequence of probability
Monte_Carlo_method
e.g. a random matrix, random tree, random sequence, random process, etc. A random matrix is a matrix-valued random element. Many important properties
Random_element
Cryptanalytic method for unauthorized users to access data
cryptography, where every cleartext bit has a corresponding key from a truly random sequence of key bits. A 140-character one-time-pad-encoded string subjected
Brute-force_attack
American mathematician and computer scientist (1903–1995)
or the Gödel Prize. Church also made contributions to the theory of random sequences. Church’s elaboration of a methodology involving the logistic method
Alonzo_Church
Topics referred to by the same term
toy Pinwheel (cryptography), a device for producing a short pseudo-random sequence of bits Pinwheel (shogi), an opening in the game shogi or Japanese
Pinwheel
Output of a dynamic system when given a brief input
input and output of a system driven with a pseudo-random sequence, such as maximum length sequences. Another approach is to take a sine sweep measurement
Impulse_response
Numbers obtained by adding the two previous ones
word – Binary sequence from Fibonacci recurrence Random Fibonacci sequence – Randomized mathematical sequence based upon the Fibonacci sequence Wythoff array –
Fibonacci_sequence
Bioengineering process
using random sequence primers. These fragments are reassembled to full length parental genes using primer-less PCR. These reassembled sequences are then
Protein_engineering
Process forming a path from many random steps
\{S_{n}\}} is called the simple random walk on Z {\displaystyle \mathbb {Z} } . This series (the sum of the sequence of −1s and 1s) gives the net distance
Random_walk
Extensions of the concept of randomness
The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution
Seven_states_of_randomness
Conjecture on zeros of the zeta function
the Riemann hypothesis is based on the observation that if μ(x) is a random sequence of "1"s and "−1"s then, for every ε > 0, the partial sums M ( x ) =
Riemann_hypothesis
Form of computer data storage
Random-access memory (RAM; /ræm/) is a form of electronic computer memory that can be read and changed in any order, typically used to store working data
Random-access_memory
frequency theory of randomness in terms of what he called the collective, i.e. a random sequence. Von Mises regarded the randomness of a collective as
History_of_randomness
Topics referred to by the same term
Poland, a village Sobol, Oklahoma, United States Sobol sequence, a kind of quasi-random sequence All pages with titles containing Sobol Sobel (disambiguation)
Sobol
Software library for the C++ programming language
However, having distinct random-access iterators offers efficiency advantages. For example, a vector would have a random-access iterator, but a list
Standard_Template_Library
1983 studio album by Kim Wilde
for Love") whereas "Dream Sequence" was one of Marty's more imaginative lyrics, describing what seems to be a random sequence of images. The cool blue
Catch_as_Catch_Can_(album)
RANDOM SEQUENCE
RANDOM SEQUENCE
Surname or Lastname
English or Scottish
English or Scottish : unexplained. Possibly, as Black suggests, a reduced form of Langdon.French : from the old Germanic personal name element Lando (see Land), via the oblique case, Landonis.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English
English : variant of Ransom.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Female
English
Pet form of English Miranda, RANDY means "worthy of admiration."Â Compare with masculine Randy.Â
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Boy/Male
English
Son of Rand.
Boy/Male
English American
Son of Rand.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Surname or Lastname
English
English : patronymic from Rand 1.
Surname or Lastname
English
English : variant of Brandon.
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
RANDOM SEQUENCE
RANDOM SEQUENCE
Male
Chinese
cautious or deep.
Boy/Male
Czech, Czechoslovakian, German
Tree; Stream
Boy/Male
Hindu
The Sun
Boy/Male
Hindu, Indian
Always Winner
Boy/Male
Arabic, Muslim
Beloved of Allah
Girl/Female
Indian
River Yamuna, Born of the Sun
Boy/Male
Assamese, Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
Spirit of the Wind
Boy/Male
Tamil
Khushaansh | கà¯à®·à®¾à®‚à®·
Khushi ka Ansh
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
The Tongue
Boy/Male
Indian, Kashmiri, Sanskrit
Knower of Meaning; Knowing; Sound; Reader
RANDOM SEQUENCE
RANDOM SEQUENCE
RANDOM SEQUENCE
RANDOM SEQUENCE
RANDOM SEQUENCE
n.
Ransom.
imp. & p. p.
of Ransom
v. i.
To go or stray at random.
v. i.
To extend or grow at random.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
adv.
In a random manner.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
Random.
n.
To exact a ransom for, or a payment on.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
n.
Extra hazard; chance; accident; random.
n.
Ransom; release.
adv.
At random; hit or miss. (Obs.)
n.
Anything driven at random.
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
a.
Cruising at random on the ocean.
p. pr. & vb. n.
of Ransom
v. i.
To wander at random; to scatter.