Geometric distribution
From Encyclopedia of Mathematics
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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=21286
Geometric distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Geometric_distribution&oldid=21286
This article was adapted from an original article by V.M. Kalinin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article