Definition

Discrete random variable XX, has Poisson distribution with parameter λ>0\lambda>0 if it has a probability mass function given by

f(k;λ)=Pr⁡[X=k]=λke−λk!f(k;\lambda) = \Pr[X=k]=\frac{\lambda^k e^{-\lambda}}{k!}

for kk occurences

References

  1. https://en.wikipedia.org/wiki/Poisson_distribution