# Geometric distribution

From Conservapedia

The **geometric distribution** is a discrete distribution which describes the
number of repetitions of a Bernoulli experiment to get a success. Therefore,
its support are the positive integers, {1,2,3,…}

## Alternative definition

Some authors describe the geometric distribution as the number of repetitions until the first success, its support being the non-negative integers {0,1,2,…}

## Mean and Variance

The mean for a random variable *X* following a geometric distribution
with a probability of success *p* (and *q* = 1 - *p*) is

The variance can be calculated similarly:

.

## Probability-generating function

The probability-generating function is:

.