rayleigh distribution
Distribution of \(Z = \sqrt{X^2 + Y^2}\) for any gaussian variables X and Y with mean 0 and equal variance, \(\sigma^2\)
Distribution with pdf \(f(x)\)
\begin{equation}
f(x) =
\begin{cases}
0 & x < 0 \\
\frac{x}{\sigma^2} e^{\frac{-x^2}{2\sigma^2}} & x \ge 0 \\
\end{cases}
\end{equation}
The expected value of this distribution is
\begin{equation}
E[x] = \sqrt{\frac{\pi}{2}} \sigma
\end{equation}