Probability & Combinatorics
Advanced

Poisson Probability

Probability of k events in a fixed interval given average rate λ.

Formula

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

Variables

\lambdaAverage rate
kEvent count

Example

Rare-event modeling like call arrivals

Did You Know?

The Poisson distribution approximates the binomial for rare events.

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