Data-Analysis-Jupyter/poisson/equations.md

P(k{\text{ events in time period}})=e^{-\frac{\text{events}}{\text{time}}*\text{time period}} * \frac{(\frac{\text{events}}{\text{time}}*{\text{time period}})^{k}}{k!}

P(k{\text{ events in interval}})=e^{-\lambda }{\frac {\lambda ^{k}}{k!}}

\frac{1 \text{ meteor}}{15 \text{ minutes}} * 60 \text{ minutes} = 4 \text{ meteors expected} = \lambda

{\displaystyle P(4{\text{ meteors in 1 hour}})=e^{-4}{\frac {4^{4}}{4!}}} = 0.195 = 19.5\%

P(T > t) = e^{-\text{rate} * {t}}

P(T \le t) = 1 - e^{-\text{rate} * {t}}

\Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}