I am a mathematics and chemistry double major and I just finished my statistics requirement and a great deal of the class was spent on probability distributions (e.g. Binomial, Poisson, Geometric, Gamma, etc.) and so I was wondering since electrons have a "probability" of being in a certain location according to the Heisenberg Uncertainty Principle, what sort of probability distribution would this represent?
As in, could we treat electrons and their positions as discrete or continuous random variables? And if so, what sort of distribution could we use for an electron being in a particular cloud?