Definition:Moment Generating Function
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Definition
Let $X$ be a random variable.
Then the moment generating function of $X$, $M_X$, is defined as:
- $\map {M_X} t = \expect {e^{t X} }$
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.
Also see
- Results about moment generating functions can be found here.