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mean
until the first success, its support being the non-negative integers
until the first success, its support being the non-negative integers
{0,1,2,…}[[category:Probability and Statistics]]
{0,1,2,…}[[category:Probability and Statistics]]
== Mean ==
The [[mean]] for a [[random variable]] ''X'' following a geometric distribution
with a probability of success ''p'' (and ''q'' = 1 - ''p'') is
<math>\mathbf{E}[X] = \sum_{n=0}^{\infty} (n+1) q^n
p</math><math>=\frac{p}{(1-q)^2}= \frac{1}{p}</math>