Difference between revisions of "Geometric distribution"
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p</math><math>=\frac{p}{(1-q)^2}= \frac{1}{p}</math> | p</math><math>=\frac{p}{(1-q)^2}= \frac{1}{p}</math> | ||
| − | + | The variance can be calculated similarly: | |
| − | <math>Var(X) = \frac{1-p}{p^2}</math> | + | <math>Var(X) = \frac{1-p}{p^2}</math>. |
Revision as of 17:35, August 3, 2010
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
![{\displaystyle \mathbf {E} [X]=\sum _{n=0}^{\infty }(n+1)q^{n}p}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b68c5fe4a407b29c0a3d12a08e6bae0fa9259358)
The variance can be calculated similarly:
.
