I've read in Elementary Stochastic Processes by Mikosch (p. 98), that it is a well known fact that:
If B is a N(0,1) R.V., $E[B^4] = 3$
I also see something equivalent (but uncited) on the wikipedia page for moments: http://en.wikipedia.org/wiki/Normal_distribution#Moments, namely that:
$E[X^P] = \sigma^P(P-1)!!$ if $P$ is even.
where $ \sigma$ is of course the standard deviation of the R.V./Distn.
Could someone please explain why this is, or link to a proof?