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Geometric distribution
(view source)
Revision as of 16:46, August 3, 2010
95 bytes added
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16:46, August 3, 2010
→Mean
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{0,1,2,…}[[category:Probability and Statistics]]
{0,1,2,…}[[category:Probability and Statistics]]
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== Mean
==
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== 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
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<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>
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Similarly, the variance can be calculated:
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<math>Var(X) = \frac{1-p}{p^2}</math>
RonLar
221
edits