Geometric distribution

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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: