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 that Xi = 1 is the same number p.
In other words, a Bernoulli process is a sequence of independent identically distributed Bernoulli trials.
Independence of the trials implies that the process is memoryless. Given that the probability p is known, past outcomes provide no information about future outcomes. (If p is unknown, however, the past informs about the future indirectly, through inferences about p.)
If the process is infinite, then from any point the future trials constitute a Bernoulli process identical to the whole process, the fresh-start property.
Read more about Bernoulli Process: Formal Definition, Finite Vs. Infinite Sequences, Binomial Distribution, As A Metric Space, As A Dynamical System, As The Cantor Space, Bernoulli Sequence, Randomness Extraction
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