Definition:Moment Generating Function

Definition
Let $X$ be a random variable.

Then the moment generating function of $X$, $M_X$, is defined as:


 * $\displaystyle M_X \left({t}\right) = \mathbb E \left[{ e^{t X} }\right]$

for all $t$ such that this expectation exists.

Also known as
The term moment generating function is commonly abbreviated to MGF or M.G.F.