How Many Goals Are Going to Be Scored in a Soccer Game?

The Poisson distribution is a distribution over all natural numbers, including 0. And so you have what I think are these three assumptions on how these events occur. First of all, they occur randomly, meaning there's not some like, "Well, I mean, that's very vague" But more specifically, they occur independently, meaning that each event doesn't care about the timing of other such events.