Random process of binary (boolean) random variables
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Bernoulli trial
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Bernoulli distribution
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Bernoulli process
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In probability and statistics, a Bernoulli 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 only two values, canonically 0 and 1. The component Bernoulli variablesXi are identically distributed and independent. Prosaically, a Bernoulli process is a repeated coin flipping, possibly with an unfair coin (but with consistent unfairness). Every variable Xi in the sequence is associated with a Bernoulli trial or experiment. They all have the same Bernoulli distribution. Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes (such as the process for a six-sided die); this generalization is known as the Bernoulli scheme.
The problem of determining the process, given only a limited sample of Bernoulli trials, may be called the problem of checking whether a coin is fair.
In probability and statistics, a Bernoulliprocess (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is...
probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution...
formalization and advanced formulation of the Bernoulli trial is known as the Bernoulliprocess. Since a Bernoulli trial has only two possible outcomes, it...
reference to Bernoulli, by Ladislaus Bortkiewicz who in 1917 wrote in German the word stochastik with a sense meaning random. The term stochastic process first...
experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulliprocess; for a single trial, i.e....
Bernoulli family of Basel. Bernoulli differential equation Bernoulli distribution Bernoulli number Bernoulli polynomials BernoulliprocessBernoulli Society...
mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulliprocess to more than two possible outcomes. Bernoulli schemes appear...
independent of the past states). A Bernoulli scheme with only two possible states is known as a Bernoulliprocess. Note, however, by the Ornstein isomorphism...
Jacob Bernoulli (also known as James in English or Jacques in French; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was one of the many prominent...
processes Basic affine jump diffusion Bernoulliprocess: discrete-time processes with two possible states. Bernoulli schemes: discrete-time processes...
of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted r...
\operatorname {H} _{\text{b}}(p)} , is defined as the entropy of a Bernoulliprocess with probability p {\displaystyle p} of one of two values. It is a...
transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)...
statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in...
statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe...
Bernoulli number Bernoulli polynomials BernoulliprocessBernoulli trial Lemniscate of BernoulliBernoulli, a journal published by the Bernoulli Society for...
average process. The Ornstein isomorphism theorem states that every stationary stochastic process is equivalent to a Bernoulli scheme (a Bernoulliprocess with...
interpreted as the Bernoulliprocess. One may generalize this to include continuous time Lévy processes, and many Lévy processes can be seen as limits...
his father Johann Bernoulli and one of his brothers, Daniel Bernoulli. He was one of the many prominent mathematicians in the Bernoulli family. Nicolaus...
continuously distributed values Basic distributions: Bernoulli distribution, for the outcome of a single Bernoulli trial (e.g. success/failure, yes/no) Binomial...
Discrete time and continuous time Continuous-time stochastic process Discrete-time stochastic process Continuous modelling Discrete modelling Continuous geometry...
This is nothing but a different way of stating the expectation of a Bernoulli random variable, as calculated in the table above. Formulas in terms of...
pseudorandom number generator, but one may also use some external physical process, such as the last digits of the time given by the computer clock. A pseudorandom...
Random variable Bernoulliprocess Continuous or discrete Expected value Variance Markov chain Observed value Random walk Stochastic process Complementary...
of coin flipping is described by means of the Bernoulliprocess; a single flip of a coin is a Bernoulli trial. In the study of statistics, coin-flipping...
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