Inspired by a simple probability puzzle, I set out to determine the probability that a Poisson random variable is divisible by a given integer, before extending this result to calculate the distribution of the Poisson random variable modulo a divisor.

Not all integrals are created equally. In this post we look at a particular class of integrals which can be highly troublesome to evaluate. Thankfully, probability theory provides us with a framework that allows us to avoid the standard method of evaluation and by doing so makes our working far less error-prone.