# Bernoulli trial

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Related to Bernoulli trial: binomial distribution, Geometric distribution

## Ber·noul·li tri·al

(bĕr-nū'lē),
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 outcome is termed a success and is assigned the score 1, the other is a failure and has the score 0. Thus the outcome might be 0 (no heads, one tail) or 1 (1 head, no tails).
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For describing discrete random variables associated with experiments, an important notion is that of Bernoulli trials. There are three characteristics that define such trials:
Consider a fixed number R of replicates of a truncated geometric experiment, each replicate r (1 [less than or equal to] r [less than or equal to] R) consisting of a maximum of T - 1 Bernoulli trials (with success probability [p.sub.a]) until [x.sup.(a).sub.r] = 1 successes are observed, and with the entire replicate discarded if a success has not occurred within the T - 1 trials.
Prediction of system performance has been historically accomplished using a statistical analysis, (1) treating the combination of periodic events and the likelihood of simultaneous events as a series of Bernoulli trials. The parameters of the receiver system are analyzed with respect to the radar signal of interest and the mean time to intercept is computed.
In this paper, we assume the existence of a noise source that delivers a continuous string of random binary values, commonly called elementary Bernoulli trials (or trials, for short).
These problems are called Bernoulli trials. Bernoulli systems have two outcomes--the outcome we want or are interested in, called a success, and the other outcome, called a failure.
of Utah)also accommodates single-semester graduate courses as he covers the basics in terms of classical probability, including discrete and conditional probability, independence, discrete distributions, absolutely continuous distributions, expectations and variance, as well as Bernoulli trials, measure theory, integration, product spaces, the central limit theorem, martingales, Brownian motion, and stochastic integration.
Bernoulli trials Trials that involve random processes for which there are only two possible outcomes that occur without any fixed pattern, and the probability of either outcome remains fixed for each trial.

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