Comparison Biomial and Poisson Distribution

Poission Distribution

\(\lambda\in\mathbb{R}^+\) is given. The densitiy function is \(P(X = k) = \dfrac{\lambda^k e^{-\lambda}}{k!}\) with \(k\in\mathbb{N}_0\)

Binomial Distribution

\(p\in[0,1]\) and \(n\in\mathbb{N}\) are given. The densitiy function is \(P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}\) with \(k\in\{0,\dots n\}\)