# Relationship binomial distribution and central limit theorem + poission distribution

1. Mar 29, 2010

### azay

From the central limit theorem the binomial distribution can be approximated by a normal distribution N(0,1). But the binomial distribution can also be approximated by a poisson distribition.

Does this mean there is a relationship between the normal distribution and the poisson distribution (especially as n->infinity in B(n,p))?

I'm confused about this. To me it sounds like the normal distribution and the poisson distribution are equal then. Or does the standardisation in the central limit theorem make the difference?

Thanks

2. Mar 29, 2010

### mathman

Re: Relationship binomial distribution and central limit theorem + poission distribut

The difference depends on how you take the limit. To get a normal from binomial, you keep p constant as n -> ∞. To get a Poisson from a binomial, you keep np constant as n -> ∞.