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Statistical Background
Published in Taesam Lee, Vijay P. Singh, Statistical Downscaling for Hydrological and Environmental Applications, 2018
In a single trial of an experiment with two possible outcomes (e.g., rain or no rain for a day), the probability distribution of two outcomes is called a Bernoulli distribution, and its trial is called a Bernoulli trial. The outcomes are also considered as occurrence or nonoccurrence, i.e., 1 or 0, respectively. It is assumed that the occurrence probability (i.e., p = p(X = 1), 0 ≤ p ≤ 1) is constant, and it is obvious that the nonoccurrence probability (i.e., p(X = 0) = 1 − p), since the outcomes are mutually exclusive.
Statistical Distributions
Published in Daniel B. Rowe, Multivariate Bayesian Statistics, 2002
A Bernoulli trial or experiment is an experiment in which there are two possible outcomes, one labeled “success” with probability ϱ, the other labeled “failure” with probability 1 − ϱ. The Binomial distribution [1, 2] gives the probability of x successes out of n independent Bernoulli trials, where the probability of success in each trial is ϱ. A Bernoulli trial is an experiment such as flipping a coin where there are only two possible outcomes.
Probability and Statistics
Published in Paul J. Fortier, George R. Desrochers, Modeling and Analysis of Local Area Networks, 1990
Paul J. Fortier, George R. Desrochers
The concept of a Bernoulli trial is important in many discrete distributions. A Bernoulli trial is an experiment in which the outcome can be only success or failure. Random variables defined on successive Bernoulli trials make up several of the discrete density functions to be discussed.
Partial sums of analytic functions defined by binomial distribution and negative binomial distribution
Published in Applied Mathematics in Science and Engineering, 2022
Rubab Nawaz, Saira Zainab, Fairouz Tchier, Qin Xin, Afis Saliu, Sarfraz Nawaz Malik
One of the most essential discrete probability distributions is Binomial distribution. When there are two possible outcomes, then Binomial distribution model is used which is an important probability model. In a Bernoulli trial, the random experiment has two hypothetical results that are success or failure. If the number of trials m = 1, then it is called Bernoulli distribution that is special case for the Binomial distribution. Binomial distribution determines the probability of successful outcomes. It has two parameters, m and p where m denotes the number of trial and p denotes the success outcomes.