The binomial distribution


This probability distribution describes the behavior of a discrete random
variable that is characterized by either a "success" result or a "failure"
result.

The value of the random variable is the result of an experiment, called the
binomial experiment.


Binomial experiment

This experiment has four characteristics:

1. It consists of n identical trials.
2. Only two outcomes are possible: success or failure.
3. The probability of success (p) does not change with trials.
4. The trials are independent.



(See images for mathematical formulas and illustration.)


Reference:

Anderson, D.R., D.J. Sweeny, and T.A. Williams (1999):  Statistics for
Business and Economics. South--Western.