# Definition:Bernoulli Process

## Definition

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.

## Source of Name

This entry was named for Jacob Bernoulli.