# Moment generating functions

Hello,

I was wondering if anyone knew how to find a moment generating function about the mean. What I want is a function whose power series expansion gives you a power series where the x^n coefficient is the nth moment about the mean. normally, moment generating functions give you the raw moment (moment about 0). I'd like to convert these to moments about the mean.

Thanks for your help!

## Answers and Replies

Hello,

I was wondering if anyone knew how to find a moment generating function about the mean. What I want is a function whose power series expansion gives you a power series where the x^n coefficient is the nth moment about the mean. normally, moment generating functions give you the raw moment (moment about 0). I'd like to convert these to moments about the mean.

Thanks for your help!

The MGF is E[e^(tX)], so to get the central moments if E[X]=m you calculate E[e^(t(X-m))]=e^(-tm)E[e^(tX)]

The MGF is E[e^(tX)], so to get the central moments if E[X]=m you calculate E[e^(t(X-m))]=e^(-tm)E[e^(tX)]

Thanks for your help, I don't know how I didn't get this on my own, ugh. Just in case someone uses this thread in the future: You still do the series expansion around 0 (not m) to get moments about a point m.