1. ## normal distribution moments

2. Hello,

Well, you can think a little about it...

The characteristic function of the normal distribution $(\xi,\sigma^2)$ is $\psi(t)=\exp\left(it\xi-\tfrac{\sigma^2t^2}{2}\right)$

Then there is that interesting property of the characteristic function :
$\mathbb{E}(X^n)=\frac{1}{i^n} \cdot \left.\frac{d^n}{dt^n} \psi(t)\right|_{t=0}$

I learnt it with the characteristic function, but you can also use the moment generating function $M(t)$ :
$\mathbb{E}(X^n)=\left.\frac{d^n}{dt^n} M(t)\right|_{t=0}$
And for the normal distribution, $M(t)=\exp\left(\xi t+\tfrac{\sigma^2t^2}{2}\right)$
It should be easier to deal with it..