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I've been revising some statistics lately, namely random variable distributions. My friend has given me some distributions he came up with and I'm trying to find the distributions of sum of variables etc.
He gave me 1/sqrt(1-x^2) and I'm pretty much stuck, because every way I know of doing this kind of problems leads me to an integral that wolfram doesn't even dare to touch.
Pic rel, I've tried the very standard method and ended up with integral that I have no idea how to solve and wolfram comes up with elliptic integrals. I've also tried to go through the cumulative distr. function but ended up later with integral of arcsin(t-x)/sqrt(1-x^2) that I can't solve either.
Any hints? Thanks.