Binomial distribution

A family of theoretical distributions that is useful as a model for some discrete random variables. Each distribution in this family gives the probability of obtaining a specified number of successes in a specified number of trials, under the following conditions:

• The number of trials, n, is fixed.
• The trials are independent of each other.
• Each trial has two outcomes: "success" and "failure".
• The probability of success in a trial, π, is the same in each trial.

Each member of this family of distributions is uniquely identified by specifying n and π. As such, n and π, are the parameters of the binomial distribution, and the distribution is sometimes written as binomial (n, π).

Let the random variable X represent the number of successes in n trials that satisfy the conditions stated above. The probability of x successes in n trials is calculated by:

Example

A graph of the probability function for the binomial distribution with n = 6 and π = 0.4 is shown below.

Curriculum achievement objectives reference

Probability: Level 8

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