In probability and statistics, a Bernoulli process or a Bernoulli experiment
is a stochastic process consisting of
finite or infinite sequence of independent random variables
X_{1}, X_{2}, X_{3},..., such that
- For each i, the value of X_{i} is either 0 or 1;
- For all values of i, the probability that X_{i}=1 is the same number p.
The two possible values of each
X_{i} are often called "success" and "failure", so that, when expressed as a number, 0 or 1, the value is said to be the number of successes on the
ith "trial".
The individual success/failure variables
X_{i} are also called
Bernoulli trials.
Random variables associated with the Bernoulli process include
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