Raw moments of Gaussian Distribution

[SeriousNoob]

I'm wondering if there was a table of moments for a Gaussian Distribution, I found one up to the fourth moment
U \sim N(\mu, \sigma^2)
E[U^2]=\mu^2+\sigma^2
E[U^3]=\mu^3+3\mu\sigma^2
E[U^4]=\mu^4+6\mu\sigma^2+3\sigma^4

I'm doing a problem right now and i need the 8th moment.

 

[mathman]

It is a straightforward (tedious) integral.

 

[abalter]

You do not need to do integrals if you know the property of the Gaussian distribution that all central moments above 2 are 0. But I'm not saying it is the easiest method. Here is how you do it for m_3:

m_3 = \left< (x-<x>)^2 \right> = <x^3> - 3<x>^3 + 3<x><x^2> + <x>^3 = <x^3> + <x>^3 + 3 <x> ( <x^2> - <x>^2) = m_3 + \mu^3 + 3<x>\sigma^2 = 0

From this we get:

m_3 = \mu \sigma^2 + \mu^3

And so on...