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
A geometric distribution of probability .
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.
Geometric distribution. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Geometric_distribution&oldid=12864