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Home > Bernoulli process

In probability and statistics, a Bernoulli process

is a discrete-time stochastic process consisting of finite or infinite sequence of independent random variables X1, X2, X3,..., such that

In other words, a Bernoulli process is a sequence of independent identically distributed Bernoulli trials. The two possible values of each Xi are often called "success" and "failure", so that, when expressed as a number, 0 or 1, the value is said to be the number of successes on the ith "trial". The individual success/failure variables Xi are also called Bernoulli trials.

Random variables associated with the Bernoulli process include


Stochastic processes

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Topics: Bernoulli Process, Bernoulli's Inequality, Bernoulli Number...

Bernoulli's inequalityBernoulli's inequality in real analysis states that : for every integer n ≥ 0 and every real number x ≥ −1. If n ≥ 0 is even, then the inequality is valid for all real numbers x''. The strict version of the inequality reads : for every inteBernoulli numberInteger sequences In mathematics, the Bernoulli numbers ''B were first discovered in connection with the closed forms of the sums : for various fixed values of n''. The closed forms are always polynomials in m of degree n 1 and are called Bernoulli polynoBernoulli's equationIn fluid dynamics, Bernoulli's equation describes the behavior of a fluid moving along a streamline. v fluid velocity along the streamline : g gravitational constant : y elevation in the direction of gravity : P pressure along the streamline : fluid densi
Bernoulli's principleBernoulli's principle states that in fluid flow, an increase in velocity happens simultaneously with decrease in pressure. It is named for the Dutch/ Swiss mathematician/scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler andBernoulli processIn probability and statistics, a Bernoulli process is a discrete-time stochastic process consisting of finite or infinite sequence of independent random variables X X X . such that For each i the value of X is either 0 or 1; For all values of i, the probaBernoulli trialIn the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, called "success" and "failure. In practice it refers to a single event which can have one of two possible o
Bernoulli distributionBernoulliBernoulli Box
Bernoulli (crater)  
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