# Binomial, Bernoulli and Poisson Distributions

**Topics:**Discrete probability distribution, Random variable, Probability theory

**Pages:**2 (493 words)

**Published:**April 23, 2012

The Binomial, Bernoulli and Poisson distributions are discrete probability distributions in which the values that might be observed are restricted to being within a pre-defined list of possible values. This list has either a finite number of members, or at most is countable.

* Binomial distribution

In many cases, it is appropriate to summarize a group of independent observations by the number of observations in the group that represent one of two outcomes. For example, the proportion of individuals in a random sample who support one of two political candidates fits this description. In this case, the statistic is the count X of voters who support the candidate divided by the total number of individuals in the group n. This provides an estimate of the parameter p, the proportion of individuals who support the candidate in the entire population. The binomial distribution describes the behavior of a count variable X if the following conditions apply: the number of observations n is fixed, each observation is independent and represents one of two outcomes ("success" or "failure") and if the probability of "success" p is the same for each outcome. If these conditions are met, then X has a binomial distribution with parameters n and p, abbreviated B(n,p).

* Bernoulli distribution

In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, is a discrete probability distribution The distribution of a discrete random variable taking two values, usually 0 and 1. An experiment or trial that has exactly two possible results, often classified as 'success' or 'failure', is called a Bernoulli trial. If the probability of a success is p and the number of successes in a single experiment is the random variable X, then X is a Bernoulli variable (also called a binary variable) and is said to have a Bernoulli distribution with parameter p. A binomial variable with...

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