The term Bernoulli sequence is often used informally to refer to a realization of a Bernoulli process. However, the term has an entirely different formal definition as given below.
Suppose a Bernoulli process formally defined as a single random variable (see preceding section). For every infinite sequence x of coin flips, there is a sequence of integers
called the Bernoulli sequence associated with the Bernoulli process. For example, if x represents a sequence of coin flips, then the associated Bernoulli sequence is the list of natural numbers or time-points for which the coin toss outcome is heads.
So defined, a Bernoulli sequence is also a random subset of the index set, the natural numbers .
Almost all Bernoulli sequences are ergodic sequences.
Read more about this topic: Bernoulli Process
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