Let's say we have a known normal distribution $N(\mu,\sigma^2)$.
I now draw 2 points $p1$ and $p2$ randomly from this Gaussian distribution for every observation, and repeat this process large number of times.
(1) What will the distribution of $p1 / p2$ look like? Will it be normal? Can we say something about it's mean and standard deviation?
(2) What will the distribution of $max(p1 / p2, p2/p1)$ look like? Will it be normal? Can we say something about it's mean and standard deviation?
(3) What will the distribution of $e^p_1 / e^p_2$ and the distribution of $max(e^p_1 / e^p_2, e^p_2/ e^p_1)$ look like? Will it be normal? Can we say something about it's mean and standard deviation?