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Difference between revisions of "Geometric distribution"

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The distribution of a discrete random variable assuming non-negative integral values <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442301.png" /> with probabilities <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442302.png" />, where the distribution parameter <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442303.png" /> is a number in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442304.png" />. The characteristic function is
 
The distribution of a discrete random variable assuming non-negative integral values <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442301.png" /> with probabilities <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442302.png" />, where the distribution parameter <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442303.png" /> is a number in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g044/g044230/g0442304.png" />. The characteristic function is
  

Revision as of 17:54, 22 February 2012

2020 Mathematics Subject Classification: Primary: 60E99 [MSN][ZBL]

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://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