How to Calculate Poisson Distribution
What is Poisson Distribution?
The Poisson distribution models the number of events in a fixed interval given average rate λ. P(X=k) = (e^−λ × λᵏ) / k!. Both the mean and variance equal λ.
Step-by-Step Guide
- 1P(X=k) = (e^−λ × λᵏ) / k!
- 2λ = average number of events per interval
- 3Events must be independent and occur at constant average rate
Worked Examples
Input
λ=3 calls/min · P(exactly 5 calls)
Result
P = e^−3 × 3⁵/120 ≈ 10.1%
Classic Poisson application
Ready to calculate? Try the free Poisson Distribution Calculator
Try it yourself →