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
x = 0, 1, 2, … , n
n = 1, 2, 3, …
p = success probability; 0 < p < 1
The trials must have the following characteristics:
- the total number of trials is fixed in advance;
- there are just two possible outcomes of each trial: success or failure;
- the outcomes of all the trials are statistically independent;
- 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)
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.