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geometric random variable

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A geometric random variable with parameter $p\in(0,1]$ is one whose density distribution function is given by

$\displaystyle f_X(x) = p(1-p)^x,\qquad x=0,1,2,\dotsc$

This is denoted by $X\sim Geo(p)$ .

Notes:

A standard application of geometric random variables is where represents the number of failed Bernoulli trials before the first success.
The expected value of a geometric random variable is given by $E[X] = \frac{1-p}{p}$ , and the variance by $Var[X] = \frac{1-p}{p^2}$
The moment generating function of a geometric random variable is given by $M_X(t) = \frac{p}{1 - (1-p)e^t}$ .

"geometric random variable" is owned by mathcam. [ full author list (2) | owner history (1) ]

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Other names:

geometric distribution

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Cross-references: moment generating function, variance, expected value, number, represents, application, distribution function, density, parameter
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This is version 9 of geometric random variable, born on 2001-10-26, modified 2007-06-24.
Object id is 520, canonical name is GeometricRandomVariable.
Accessed 15409 times total.

Classification:

AMS MSC:	60-00 (Probability theory and stochastic processes :: General reference works )
	62-00 (Statistics :: General reference works )

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