Poisson Distribution Calculator
Calculate Poisson probabilities for a given mean rate and number of events. Useful for modeling rare events.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Poisson Distribution Calculator
- Enter the Mean Rate (λ): Input the average number of events occurring in the fixed interval (e.g., 2.5). This must be a non-negative number.
- Enter the Number of Events (k): Input the specific count of events you want to calculate the probability for (e.g., 3). This must be a non-negative integer (whole number).
- Click "Calculate Probability": Press the button to compute the result.
- Read the Result: The calculator displays the exact probability P(X = k) and shows the formula used.
Example: To find the probability of exactly 3 events when the average rate is 2.5, enter λ = 2.5 and k = 3. The result will be P(X = 3) ≈ 0.2138.
Note: All inputs must be non-negative. The calculator uses the standard Poisson formula: P(X=k) = (e-λ × λk) / k!
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Frequently Asked Questions
The Poisson distribution models the number of events occurring in a fixed interval of time or space, given a constant mean rate.
The result is the probability of observing exactly the specified number of events, assuming the events occur independently at a constant average rate.
Yes, the Poisson distribution is particularly useful for modeling rare events, such as accidents or defects.
