I've been thinking about problem that, conceptually is very simple. I have two random variables $F_{x}$ and $F_{y}$ both of which follow a Gaussian distribution of mean $0$ and variance $1$. Now, I wish to compute the expectation value, $\langle\sqrt{F_{x}^2 + F_{y}^2}\rangle$. It's been more than a while since I did any probability theory and am wondering if there is an easy way of doing this. I keep on running into nasty integrals, but I may be approaching the problem from the wrong direction.
Thanks,