# Geometric distribution

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The distribution of a discrete random variable assuming non-negative integral values with probabilities , where the distribution parameter is a number in . The characteristic function is

the mathematical expectation is ; the variance is ; the generating function is

Figure: g044230a

A geometric distribution of probability .

Figure: g044230b

The distribution function .

The random variable equal to the number of independent trials prior to the first successful outcome with a probability of success and a probability of failure has a geometric distribution. The name originates from the geometric progression which generates such a distribution.

How to Cite This Entry:
Geometric distribution. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Geometric_distribution&oldid=12864
This article was adapted from an original article by V.M. Kalinin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article