e-Statistics > 4470-5470 Probability and Statistics I

Poisson distribution

The Poisson distribution with parameter $ \lambda =$ ( $ \lambda > 0$) has the frequency function

$\displaystyle p(k) = e^{-\lambda} \frac{\lambda^k}{k!},
\quad k = 0,1,2,\ldots
$

Binomial distribution (blue bars) with parameter $ n=$ and $ p =$ can be approximated by a Poisson distribution (bars of green shading) with parameter $ \lambda = np$ when $ n$ is large and $ p$ is small enough for $ \lambda$ to become a moderate number.