The Poisson distribution gives the probability of each possible number of occurrences of an event happening within a given interval, specifically for events that are independent but happen with a fixed probability per unit time. It is named for French mathematician Siméon Denis Poisson.
f(k;λ) = probability(X = k) λke-λ = —————— k!
For example, if something occurs on average 1.1 times per second (i.e., λ=1.1), then the probability of 6 occurrences within some specific second (i.e., k=6) is:
1.16e-1.1 ————————— 6!