A Bernoulli process is a sequence of Bernoulli trials
in which:
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 constitute "success" or an event. It is unlikely that the factory owner would think of this as a successful outcome!
- the trials are independent of each other,
- there are only two possible outcomes for each
trial, arbitrarily labeled "success" or "failure"
- the probability of success is the same for each
trial.
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 constitute "success" or an event. It is unlikely that the factory owner would think of this as a successful outcome!
