Definition:Geometric Distribution/Formulation 1

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

$X$ 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 $0 < p < 1$.

It is written:

$X \sim \Geometric p$

Also presented as

The geometric distribution can also be found presented as:

$\map \Pr {X = k} = p^k q$

where $q = 1 - p$.

Also see

  • Results about the geometric distribution can be found here.

Technical Note

The $\LaTeX$ code for \(\Geometric {p}\) is \Geometric {p} .

When the argument is a single character, it is usual to omit the braces:

\Geometric p