Bernoulli trial


Bernoulli trial

In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure".

In practice it refers to a single experiment which can have one of two possible outcomes. These events can be phrased into "yes or no" questions:

*Did the coin land "heads"?
*Was the newborn child a girl?
*Were a person's eyes green?
*Did a mosquito die after the area was sprayed with insecticide?
*Did a potential customer decide to buy a product?
*Did a citizen vote for a specific candidate?
*Did an employee vote pro-union?

Therefore success and failure are labels for outcomes, and should not be construed literally. Examples of Bernoulli trials include

*Flipping a coin. In this context, obverse ("heads") conventionally denotes success and reverse ("tails") denotes failure. A fair coin has the probability of success 0.5 by definition.
*Rolling a die, where a six is "success" and everything else a "failure".
*In conducting a political opinion poll, choosing a voter at random to ascertain whether that voter will vote "yes" in an upcoming referendum.

Mathematically, such a trial is modeled by a random variable which can take only two values, 0 and 1, with 1 being thought of as "success". If "p" is the probability of success, then the expected value of such a random variable is "p" and its standard deviation is

:sqrt{p(1-p)}.,

A Bernoulli process consists of repeatedly performing independent but identical Bernoulli trials.

The process of determining an expectation value and deviation, based on a limited number of Bernoulli trials is colloquially known as "checking if a coin is fair".

ee also

*Bernoulli distribution
*Bernoulli scheme
*Bernoulli sampling
*Binomial Distribution
*Poisson sampling
*Sampling design
*Coin flipping


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