Suppose I have something like a targeting problem, where I specify an angular dispersion in the up and down direction with two Gaussian distributions, each having a mean of 0 and a std of 0.3 degrees.
As I understand it, the square root of the squares of the random variable pairs from these distributions would form a Rayleigh Distribution, defining the distribution of the dispersion with a single angle. Is this correct?
If so, how can I compute the mean and std of the resulting Rayleigh distribution, using the means and stds of the two original Gaussian distributions?
What if I started with a Rayleigh Distribution? How would I go backwards to break it into the two Gaussians?