Category:Definitions/Geometric Distribution

This category contains definitions related to Geometric Distribution.
Related results can be found in Category:Geometric Distribution.

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

Then $X$ obeys a geometric distribution if and only if $\map Pr {X = k}$ decreases in geometric progression as $k$ increases.

There are vrious formulations of the geometric distribution:

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 $0 < p < 1$.