Binomial distribution

related topics
{math, number, function}
{rate, high, increase}
{law, state, case}
{math, energy, light}

In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial. In fact, when n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

It is frequently used to model number of successes in a sample of size n from a population of size N. If the samples are not independent (this is sampling without replacement), the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution is a good approximation, and widely used.

Contents

Examples

An elementary example is this: roll a standard die ten times and count the number of fours. The distribution of this random number is a binomial distribution with n = 10 and p = 1/6.

As another example, flip a coin three times and count the number of heads. The distribution of this random number is a binomial distribution with n = 3 and p = 1/2.

Full article ▸

related documents
Conditional probability
Average
Interpolation search
Rank (linear algebra)
Cumulative distribution function
Measure (mathematics)
Algorithms for calculating variance
Bolzano–Weierstrass theorem
Linear search
Union (set theory)
Constructible number
Arity
Compactness theorem
Procedural programming
Closure (topology)
Integral domain
Pauli matrices
Riesz representation theorem
Octal
Compact space
Decimal
Elliptic integral
Chain complex
Perfect number
Gram–Schmidt process
Hyperbolic function
Depth-first search
Free variables and bound variables
Legendre polynomials
Open set