Difference between revisions of "Geometric distribution"
From Conservapedia
(→Probability-generating function: def. of prob.gen.fct.) |
m |
||
| Line 6: | Line 6: | ||
Some authors describe the geometric distribution as the number of repetitions | Some authors describe the geometric distribution as the number of repetitions | ||
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,…} | + | {0,1,2,…} |
== Mean and Variance == | == Mean and Variance == | ||
| Line 23: | Line 23: | ||
<math>G_X(z) = \frac{z\,p}{1-z(1-p)}</math>. | <math>G_X(z) = \frac{z\,p}{1-z(1-p)}</math>. | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | [[category:Probability and Statistics]] | ||
Revision as of 13:43, August 14, 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
The variance can be calculated similarly:
.
Probability-generating function
The probability-generating function 
is:
.
