Blurb::
Aleatory uncertain discrete variable - binomial

Description::
The binomial distribution describes probabilities associated with a series
of independent Bernoulli trials.
A Bernoulli trial is an event with two mutually exclusive outcomes,
such as 0 or 1, yes or no, success or fail.
The probability of success remains the same (the trials are independent).

The density function for the binomial distribution is given by:

.. math:: f(x) = \left(\begin{array}{c}n\\x\end{array}\right){p^x}{(1-p)^{(n-x)}},

where :math:`p` is the probability of failure per trial,  :math:`n` is the number of trials and :math:`x` is the number of successes.

Topics::
discrete_variables, aleatory_uncertain_variables

Examples::

Theory::
The binomial distribution is typically used to predict the number of failures
or defective items in a total of :math:`n` independent tests or trials,
where each trial has the probability :math:`p` of failing or being defective.

Faq::

See_Also::
