User:MegaXun/sandbox

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 p that Xi = 1 is the same. 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.