Poisson Distribution Calculator
Calculate P(X=k) = (lambda^k * e^(-lambda)) / k!.
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Enter the average rate (lambda) and the number of events (k). Lambda is the expected number of events in a given interval. The calculator computes P(X=k), cumulative probabilities, and distribution statistics instantly.
About This Calculator
The Poisson distribution models the number of events occurring in a fixed interval when events happen independently at a constant average rate. It is used for modeling rare events: call center arrivals, website visits per minute, defects per unit, radioactive decay. The mean and variance are both equal to lambda.
Frequently Asked Questions
When should I use the Poisson distribution?
Use it when counting events in a fixed interval (time, area, volume), events are independent, and the average rate is constant. Common examples: emails per hour, accidents per month, typos per page.
What is the relationship between Poisson and binomial?
The Poisson distribution approximates the binomial when n is large and p is small (lambda = np). It is the limit of the binomial distribution.
Can lambda be a decimal?
Yes. Lambda is the average rate, so it can be any positive number, such as 3.7 events per hour.