# Definition:Geometric Distribution/Formulation 1

Jump to navigation
Jump to search

## Definition

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

- Bernoulli Process as Geometric Distribution: the model of the number of successes achieved in a series of Bernoulli trials before the first failure is encountered.

- 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`

## Sources

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.If you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**geometric distribution**