Editing Coupling (probability) (section)

{{Short description|Proof technique in probability theory}}
{{other uses|Coupling (disambiguation)}}

In [[probability theory]], '''coupling''' is a [[mathematical proof|proof]] technique that allows one to compare two unrelated random variables (distributions) {{mvar|X}} and {{mvar|Y}} by creating a [[random vector]] {{mvar|W}} whose [[Marginal distribution|marginal distributions]] correspond to {{mvar|X}} and {{mvar|Y}} respectively. The choice of {{mvar|W}} is generally not unique, and the whole idea of "coupling" is about making such a choice so that {{mvar|X}} and {{mvar|Y}} can be related in a particularly desirable way.