Definition
Independent repeated trials of an experiment with two outcomes only are called Bernoulli trials. Call one of the outcomes "success" and the other outcome "failure". Let be the probability of success in a Bernoulli trial. Then the probability of failure is given by
- .
Random variables describing Bernoulli trials are often encoded using the convention that 1 = "success", 0 = "failure".
Closely related to a Bernoulli trial is a binomial experiment, which consists of a fixed number of statistically independent Bernoulli trials, each with a probability of success, and counts the number of successes. A random variable corresponding to a binomial is denoted by, and is said to have a binomial distribution. The probability of exactly successes in the experiment is given by:
- .
Bernoulli trials may also lead to negative binomial distributions (which count the number of successes in a series of repeated Bernoulli trials until a specified number of failures are seen), as well as various other distributions.
When multiple Bernoulli trials are performed, each with its own probability of success, these are sometimes referred to as Poisson trials.
Read more about this topic: Bernoulli Trial
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