## Binomial Distribution

A binomial random variable is the number of successes in a series of trials, for example, the number of ‘heads’ occurring when a coin is tossed 50 times.

A discrete random variable X is said to follow a Binomial distribution with parameters n and p if it has probability distribution

where

x = 0, 1, 2, … , n

n = 1, 2, 3, …

p = success probability; 0 < p < 1

The trials must have the following characteristics:

1. the total number of trials is fixed in advance;
2. there are just two possible outcomes of each trial: success or failure;
3. the outcomes of all the trials are statistically independent;
4. all the trials have the same probability of success.

Mean (µ) of the Binomial Distribution:

µ = np

Variance (σ2) of the Binomial Distribution:

σ2 = np(1-p)

Source:

Easton, V. J., McColl, J.H. (September 1997). Statistics Glossary – random variables and probability distributions. Retrieved December 2, 2006 from http://www.stats.gla.ac.uk/steps/glossary/probability_distributions.html#binodistn.