Binomial distribution

Binomial(n, p)

Consider an event—such as a coin coming down heads—that can be true or false in each trial—or each toss—with probability «p» -- it has a Bernoulli distribution. A binomial distribution describes the number of times an event is true -- e.g., the coin is heads -- in «n» independent trials—or tosses—where the event occurs with probability «p» on each trial.

The Binomial distribution is a non-negative discrete distribution where the probability of outcome k is given by

[math]\displaystyle{ P_{n,p}(k) = \left(\begin{array}{c}n\\k\end{array}\right) p^k (1-p)^{n-k} }[/math]

This analytic probability is computed by the library function Prob_Binomial, and the cumulative probability by CumBinomial.

The distribution has a Mean of n*p and a Variance of n*p*(1-p).

Example

An example of a binomial distribution:

Library

Distributions

See Also

• CumBinomial -- the analytica cumulative probability function for Binomial
• Prob_Binomial -- the analytic probability function for Binomial
• CumBinomialInv -- the analytica inverse cumulative probability function for Binomial
• Multinomial -- A generalization of Binomial in which more than two outcomes are possible.
• Poisson(mean)
• NegativeBinomial -- the two other common discrete distributions on the non-negative integers