This is a Gaussian bell (aka normal distribution).
Its square, I belive looks the same. Yet, I see that chi-square distribution, which is a sum of k such bell squares, looks like
Take a look at yellow chi-squared, with k=1. It should be just single bell squared. But, it looks like a hyperbola instead of Gaussian. Why?
PS I read that normally-distributed signal generates a uniformly distributed power. Is it the same kind of magic?