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{0,1,2,…}[[category:Probability and Statistics]]

{0,1,2,…}[[category:Probability and Statistics]]

== Mean ==

== Mean and Variance ==

The [[mean]] for a [[random variable]] ''X'' following a geometric distribution

The [[mean]] for a [[random variable]] ''X'' following a geometric distribution

with a probability of success ''p'' (and ''q'' = 1 - ''p'') is

with a probability of success ''p'' (and ''q'' = 1 - ''p'') is

<math>\mathbf{E}[X] = \sum_{n=0}^{\infty} (n+1) q^n

<math>\mathbf{E}[X] = \sum_{n=0}^{\infty} (n+1) q^n

p</math><math>=\frac{p}{(1-q)^2}= \frac{1}{p}</math>

p</math><math>=\frac{p}{(1-q)^2}= \frac{1}{p}</math>