# Math Help - Poisson approximation

1. ## Poisson approximation

For a Binomial distribution to be approximated to Poisson (law of large numbers).
n should be big and p should be small.

In the proof I can see why n must be big,
but can some explain to me why must the probability be small?

2. so that np converges to lambda
the mean of both distributions are np and lambda, respectively
if p didn't go to zero inversely to n, then the mean would explode and you couldn't converge
to a distribution with a finite mean like a Poisson