# 7. Poissonization¶

A binomial $$(n, p)$$ random variable has a finite number of values: it can only be between 0 and $$n$$. But now that we are studying the behavior of binomial probabilities as $$n$$ gets large, it is time to move from finite outcome spaces to spaces that are infinite.

Our first example of a probability distribution on infinitely many values is motivated by the approximation we have developed for the binomial $$(n, p)$$ distribution when $$n$$ is large and $$p$$ is small. This is the family of Poisson distributions, which has powerful relations with many other distribution families.