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Poisson Approximation

In Probability,

(nx)=n!x!(nโˆ’x)!{n \choose x} = {n! \over x! (n-x)!}
b(n,p)=Poisson(ฮป)ย whereย ฮป=npb(n, p) = \text{Poisson}(\lambda) ~ \text{where} ~ \lambda = np
nโ‰ซ1ย andย pโ‰ช1n \gg 1 ~\text{and} ~ p \ll 1

approximates binomial distribution.


bโ†’pโ€…โ€ŠโŸบโ€…โ€Šnโ‰ซ1ย &ย pโ‰ช1ย &ย ฮป=npb \rightarrow p \iff n \gg 1 ~ \& ~ p \ll 1 ~ \& ~ \lambda = np

where bb is binomial and pp is poisson