Statistics & Probability
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Poisson Distribution

Probability of k events in a fixed interval.

Formula

P(X=k)=λke−λk!P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}

Variables

\lambdaAverage rate
kEvent count

Example

If a call centre averages λ = 3 calls/min, P(0 calls in a minute) = e⁻³ ≈ 0.05.

Did You Know?

The Poisson distribution was first used to model the number of Prussian soldiers killed by horse kicks per year.

poissondistribution