# Geometric distribution

2010 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://www.encyclopediaofmath.org/index.php?title=Geometric_distribution&oldid=21286