Definition:Moment Generating Function

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Let $X$ be a random variable.

Then the moment generating function of $X$ is defined and denoted 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.