moment generating function

Given a random variableMathworldPlanetmath X, the moment generating function of X is the following function:

MX(t)=E[etX] for tR (if the expectation converges).

It can be shown that if the moment generating function of X is defined on an interval around the origin, then


In other words, the kth-derivative of the moment generating function evaluated at zero is the kth moment of X.

Title moment generating function
Canonical name MomentGeneratingFunction
Date of creation 2013-03-22 11:53:51
Last modified on 2013-03-22 11:53:51
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 10
Author mathcam (2727)
Entry type Definition
Classification msc 60E05
Classification msc 46L05
Classification msc 82-00
Classification msc 83-00
Classification msc 81-00
Related topic CharacteristicFunction2
Related topic CumulantGeneratingFunction