## MATH318: Binomial Distribution Facts

A *binomial experiment* is a probability experiment with
the following properties:
- The experiment consists of n identical trials.
- Each trial has two possible outcomes, which we'll call "success" and "failure".
- The probability of success is the same on every trial.
- The trials are independent events; the outcome of each trial is not affected by the outcomes of the other trials.

Let x be the number of successes in a binomial experiment. Then x is
a discrete random variable. The probability distribution associated
with x is called a *binomial probability distribution*.

The value of this probability distribution function is given by:

P(x=a) = f(a) = p^{a} * (1-p)^{n-a} * (n!) / ((n-a)! * (a!))
The factorial function is defined as the product:

m! = m * (m-1) * (m-2) . . . 3 * 2 * 1.