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
Famous quotes containing the word definition:
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)