\begin{definition}[Definition:Bernoulli Process]
A '''Bernoulli process''' is a sequence (either finite or infinite) of Bernoulli trials, each of which has the same parameter $p$.
That is, '''Bernoulli process (with parameter $p$)''' is a sequence $\left \langle {X_i}\right \rangle$ (either finite or infinite) such that:
* The value of each $X_i$ is one of two values (for example: $a$ or $b$).
* The probability that $X_i = a$ is the same for all $i$ (for example: $p$).
That is, it is a sequence of experiments, all of which can be modelled by the same Bernoulli distribution.
Note: The assumption is that the outcomes of all the Bernoulli trials are independent.
{{NamedforDef|Jacob Bernoulli|cat=Bernoulli, Jacob}}
Category:Definitions/Probability Theory
\end{definition}