# Binomial Distribution

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Related to Binomial Distribution: Poisson distribution, normal distribution

## Binomial Distribution

The distribution of successes and failures of a certain number of Bernoulli trials. A Bernoulli trial is a test in which there are precisely two random outcomes: success and failure. For example, if one is testing whether flipping a coin will result in heads, the two outcomes are yes (success) or no (failure). A binomial distribution, then, would be the number of heads compared to the number of tails in a given number of flips. It is also called a Bernoulli distribution.
References in periodicals archive ?
On the distributions obtained by varying the number of trials in a binomial distribution.
We used the negative binomial distributions fitted to the Ebola transmission data for the offspring distribution.
The results provide an estimate of the number of funds expected to win as a result of skill using the standard binomial distribution.
Binomial Md CI: median confidence intervals according to the binomial distribution, Mks Md CI: median confidence intervals by McKean and Schraeder's estimation, MJ Md CI: median confidence intervals by Marizt and Jarret's estimation and k Md CI: median confidence intervals by the adaptive-kernel estimation.
On the basis of the analysis of the binomial distribution, it becomes clear that 49 cases marked the choices very much, much, or moderate.
This finding was analogous to the work of Pollard et al (1977) when fitting the negative binomial distribution to groups of players.
Sarabia and Castillo  have pointed out that this distribution is conjugate prior for the binomial distribution.
Further, Nevins and Whitney describe the process as having a binomial distribution with the number of good items as the binomial random variable and the probability of a good item as the process capability "y," which is expressed as .
Over an infinite number of such trials, each combination is expected to be equally frequent (1/4 each); equivalently, the number of boys (or girls) follows a binomial distribution with n = 2 and p = 0.
If the population is large and the sample size is small relative to the population, the binomial distribution is a good approximation of the hypergeometric distribution.
The normal approximation of a binomial distribution will also be applied to estimate the minimum difficulty of the criterion test item through a control P--chart technique (Alwan, 2000).
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