Poisson distribution formula: P(k; λ) = (λ^k * e^(-λ)) / k!
Poisson distribution
Poisson distribution formula: P(k; λ) = (λ^k * e^(-λ)) / k!
The Poisson distribution formula calculates the probability of observing k events in a fixed interval when events occur independently at a constant mean rate λ. This formula is essential for understanding the likelihood of various outcomes in scenarios modeled by Poisson processes.
Example
If a bookstore averages 3 sales per hour (λ = 3), the probability of exactly 2 sales in the next hour (k = 2) is calculated using the Poisson formula: P(2; 3) = (3^2 * e^(-3)) / 2! = (9 * e^(-3)) / 2 ≈ 0.224.
Remember this
Understanding the Poisson distribution formula is crucial for accurately predicting event probabilities in fields like telecommunications, insurance, and traffic flow management.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
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