# Bernoulli trial

In the theory of

probability andstatistics , 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 theexpected value of such a random variable is "p" and itsstandard 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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**Bernoulli trial**— noun Etymology: Jacques Bernoulli died 1705 Swiss mathematician Date: 1951 one of the repetitions of a statistical experiment having exactly two mutually exclusive outcomes each with a constant probability of occurrence … New Collegiate Dictionary**bernoulli trial**— noun Usage: usually capitalized B Etymology: after Jacques Bernoulli : one of the repetitions of a statistical experiment having two mutually exclusive outcomes with constant probability of occurrence … Useful english dictionary**Bernoulli trial**— A single random event for which there are two and only two possible outcomes that are mutually exclusive and have a priori fixed (and complementary) probabilities of resulting. The trial is the realization of this process. Conventionally one… … Medical dictionary**Bernoulli**— can refer to: *any one or more of the Bernoulli family of Swiss mathematicians in the eighteenth century, including: ** Daniel Bernoulli (1700–1782), developer of Bernoulli s principle ** Jakob Bernoulli (1654–1705), also known as Jean or Jacques … Wikipedia**Bernoulli process**— In probability and statistics, a Bernoulli processis a discrete time stochastic process consisting ofa sequence of independent random variables taking values over two symbols. Prosaically, a Bernoulli process is coin flipping, possibly with an… … Wikipedia**Bernoulli sampling**— In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population that is sampled is subjected to an independent Bernoulli trial which determines whether the element becomes part of the… … Wikipedia**Bernoulli family**— The Bernoullis were a family of traders and scholars from Basel, Switzerland. The founder of the family, Leon Bernoulli, immigrated to Basel from Antwerp in the Flanders in the 16th century.The Bernoulli family has produced many notable artists… … Wikipedia**Bernoulli distribution**— Probability distribution name =Bernoulli type =mass pdf cdf parameters =1>p>0, pinR support =k={0,1}, pdf = egin{matrix} q=(1 p) mbox{for }k=0 p mbox{for }k=1 end{matrix} cdf = egin{matrix} 0 mbox{for }k … Wikipedia**Trial (disambiguation)**— A trial is, in the most general sense, a test, usually a test to see whether something does or does not meet a given standard.It may refer to: *Trial (law), the presentation of information in a formal setting, usually a court *Sea trial, the… … Wikipedia**Bernoulli distribution theorem trial**— Ber·noul·li distribution, theorem, trial (bər nooґle) (bār noo eґ) [Jakob Bernoulli, Swiss mathematician, 1654â€“1705] see under distribution, theorem, and trial … Medical dictionary