Binomial distribution

Binomial Distribution

The Binomial Distribution (pronounced: /bɪˈnoʊmiəl dɪstrɪˈbjuːʃən/) is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials with the same probability of success. The term "binomial distribution" is derived from the Latin words 'bi-' meaning two and 'nomial' meaning terms.

Definition

A Random variable X that counts the number of successes in n Bernoulli trials is said to have a binomial distribution. It is denoted by B(n, p), where n is the number of trials and p is the probability of success in a single trial.

Properties

The binomial distribution has the following properties:

• The mean of the distribution (μ) is equal to n * p.
• The variance (σ^2) is n * p * (1 - p).
• The standard deviation (σ) is the square root of the variance.

Related Terms

• Probability distribution
• Bernoulli trial
• Random variable
• Mean
• Variance
• Standard deviation

See Also

• Poisson distribution
• Normal distribution
• Geometric distribution
• Negative binomial distribution

External links

• Medical encyclopedia article on Binomial distribution
• Wikipedia's article - Binomial distribution

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