# Definitions for **bernoulli distribution**

### This page provides all possible meanings and translations of the word **bernoulli distribution**

### Princeton's WordNet

binomial distribution, Bernoulli distribution(noun)

a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success

### Wiktionary

Bernoulli distribution(Noun)

A discrete probability distribution, which takes value 1 with success probability and value 0 with failure probability .

### Freebase

Bernoulli distribution

In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, is a discrete probability distribution, which takes value 1 with success probability and value 0 with failure probability . So if is a random variable with this distribution, we have: A classical example of a Bernoulli experiment is a single toss of a coin. The coin might come up heads with probability and tails with probability . The experiment is called fair if, indicating the origin of the terminology in betting. The probability mass function of this distribution is This can also be expressed as The expected value of a Bernoulli random variable is, and its variance is Bernoulli distribution is a special case of the Binomial distribution with . The kurtosis goes to infinity for high and low values of, but for the Bernoulli distribution has a lower kurtosis than any other probability distribution, namely −2. The Bernoulli distributions for form an exponential family. The maximum likelihood estimator of based on a random sample is the sample mean.

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"bernoulli distribution." *Definitions.net.* STANDS4 LLC, 2014. Web. 29 Nov. 2014. <http://www.definitions.net/definition/bernoulli distribution>.