Bernoulli Process

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Bernoulli Process

A #~{Bernoulli process} is a sequence of Bernoulli trials in which:

  • the trials are independent of each other,
  • there are only two possible outcomes for each trial, arbitrarilly labeled "success" or "failure"
  • the probability of success is the same for each trial.

One of the simplest and most used examples of a Bernoulli process is a sequence of coin tosses where, for example, a "head" would constitute a success.

As a random process, we will regard a "success" as the occurrence of an event. There is no value judgement involved in this term, for example suppose a manufacturing machine was observed over a period of time, and we were interested in how many days the machine had broken down. If the probability of breaking down was the same each day, then we could use a Bernoulli process to model this, where the machine breaking down at least once on a particular day would constitue "success" or an event. It is unlikey that the factory owner would think of this as a successful outcome!