Category:Geometric Distribution

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This category contains results about the geometric distribution.
Definitions specific to this category can be found in Definitions/Geometric Distribution.


Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.


Formulation 1

$X$ has the geometric distribution with parameter $p$ if and only if:

$\map X \Omega = \set {0, 1, 2, \ldots} = \N$
$\map \Pr {X = k} = \paren {1 - p} p^k$

where $0 < p < 1$.


Formulation 2

$X$ has the geometric distribution with parameter $p$ if and only if:

$\map X \Omega = \set {0, 1, 2, \ldots} = \N$
$\map \Pr {X = k} = p \paren {1 - p}^k$

where $0 < p < 1$.