## Binomial distribution

Tossing a coin is an example of independent trial where head (red face) or tail (blue face) are the two possible outcomes. When it is tossed repeatedly, the experiment yields the number of successes (red faces).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 .