Editing Random variable (section)

===Equality in distribution===

If the sample space is a subset of the real line, random variables ''X'' and ''Y'' are ''equal in distribution'' (denoted <math>X \stackrel{d}{=} Y</math>) if they have the same distribution functions:
:<math>\operatorname{P}(X \le x) = \operatorname{P}(Y \le x)\quad\text{for all }x.</math>

To be equal in distribution, random variables need not be defined on the same probability space. Two random variables having equal [[moment generating function]]s have the same distribution. This provides, for example, a useful method of checking equality of certain functions of [[Independent and identically distributed random variables|independent, identically distributed (IID) random variables]]. However, the moment generating function exists only for distributions that have a defined [[Laplace transform]].