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Bernoulli process

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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 X1, X2, X3,..., such that

  • For each i, the value of Xi is either 0 or 1;
  • For all values of i, the probability that Xi=1 is the same number p.
The two possible values of each Xi 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 Xi are also called Bernoulli trials.

Random variables associated with the Bernoulli process include

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