When an experiment involves a ``Bernoulli trial'' such that
- it results in possibly two outcomes, say ``success'' or ``failure,'' and
- it is repeatedly and independently performed (that is, each trial is designed to be identical but does not interfere with others),
In the experiment the sum of successes is the random variable of interest. The exact frequency function is formulated as
for ,and it is called a binomial distribution with parameters and .