# Thread: MGF Standard Normal to Normal

1. ## MGF Standard Normal to Normal

Hi,

I'm just doing some review problems and I've found the MGF of a standard normal random variable, X ~ N(0,1). After some tedious algebra, I found it to be Mx(t) = exp(t^2 / 2).

Is there a way I can use this result to get the MGF of a regular normal random variable, X ~ N(Mu, sigma^2)?

Cheers,

2. ## Re: MGF Standard Normal to Normal

When X ~ N(0,1) , Y=Mu+ sigma *X ~ N(Mu,sigma^2)
There are properties of MGF ( you can see in wiki or google)
Mx(t) = exp(t^2 / 2).
My(t) = exp(Mu*t) Mx(sigma*t)

3. ## Re: MGF Standard Normal to Normal

Thanks Vinux, I eventually flipped back to my text to review the properties (was working from a single page of suggested problems).

Cheers!

4. ## Re: MGF Standard Normal to Normal

Also note that those MGF properties aren't specific to the normal distribution. If you have a location-scale transformation an analogous result holds.

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