Statistics calculator
Poisson Probability Calculator
Calculate exact and at-most Poisson probability from average event rate and event count.
FormulaP(X = k) = e^-lambda x lambda^k / k!
Formula
Poisson probability
This assumes events occur independently at a stable average rate.
P(X = k) = e^-lambda x lambda^k / k!
Average rate 4 and exactly 2 events gives a Poisson probability.
FAQ6 common questions for this calculator.
FAQs
What is lambda?+
Lambda is the expected average number of events in the chosen interval.
What does at most k mean?+
It sums probabilities from zero events through k events.
How does the Poisson Probability Calculator calculate the result?+
For the Poisson Probability Calculator, it uses the Poisson probability: P(X = k) = e^-lambda x lambda^k / k!. Average rate 4 and exactly 2 events gives a Poisson probability.
What information do I need to use the Poisson Probability Calculator?+
For the Poisson Probability Calculator, enter average event rate and event count. Keep the units consistent with the calculator fields and compare your setup with the worked example on the page.
How accurate is the Poisson Probability Calculator?+
Poisson Probability Calculator calculates the selected statistic from the sample values provided. It uses the Poisson probability, but missing data, outliers, sample bias, and distribution assumptions can affect what the result means.
What should I check before using the Poisson Probability Calculator result?+
For the Poisson Probability Calculator, check average event rate and event count, sample definition, missing values, outliers, and rounding precision. A statistic can be numerically correct but still describe a weak sample.
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How to use the Poisson Probability Calculator
Calculate exact and at-most Poisson probability from average event rate and event count. The page also explains the poisson probability and shows a practical example: Average rate 4 and exactly 2 events gives a Poisson probability.
- 1
Enter your details
Enter average event rate and event count, then complete any other fields shown in the calculator.
- 2
Check the calculation
Review the result alongside the poisson probability: P(X = k) = e^-lambda x lambda^k / k.
- 3
Compare scenarios
Change one or more inputs to see how they affect the poisson Probability Calculator result before you use the estimate.