User:GeorgePan1012/Bernoulli process

Lead
In probability and statistics, a Bernoulli process 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 variables Xi are identically distributed and independent. Prosaically, a Bernoulli process is a repeated coin flipping, possibly with an unfair coin. 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 dice); this generalization is known as the Bernoulli scheme.

Article body
A Bernoulli process is a finite or infinite sequence of independent random variables X1, X2, X3, ..., such that


 * for each i, the value of Xi is either 0 or 1;
 * for all values of i, the probability p that Xi = 1 is the same.