Poisson Distribution Calculator
Probabilities for counts of rare events in a fixed interval — with rate λ.
Models arrivals per hour, typos per page, calls per minute… Example: λ = 4 calls/hour, P(X = 2).
① Answer
② Steps
③ Why it works
The Poisson distribution counts events in a fixed window when they occur randomly at a constant average rate λ. The PMF e−λλk/k! balances two forces: λk/k! rewards counts near the mean while e−λ normalizes. Mean = variance = λ. It is also the limit of Binomial(n, λ/n) as n → ∞.