# Math Help - normal distribution moments

1. ## normal distribution moments

Please see the attached

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..

3. Thanks for the answer

4. Hi again,
Originally Posted by Bjorn
Thanks for the answer
I recall your initial message.
The reason why I don't want to give you the solution straightforwardly is that there is no interest in it.
And moreover, it's just simple calculations. I gave you all the formulae you need.

If you didn't see these methods, then I can't see how you are supposed to solve this. It's you who have to show me what you may be supposed to use, what you know, what you think about the problem, how you think it should be solved. You must have some background in probability, and seeing your previous threads, that's not a so basic level.

It is certainly not that I don't want to help. I spent 10 minutes in constructing my previous message (remembering the formula, checking in wikipedia if I'm not wrong, correcting the typos... xD), that's not neglectible for me. But trust me, you'll feel better if you find the solution by yourself