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Poisson Exact Count Probability Calculator — result sheet
Calculate the exact probability of observing a selected event count under a Poisson rate model.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(X=k)=e^(−λ)λ^k/k!.
The exact-count probability is evaluated from one nonnegative rate and a whole-number event count.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Average event rate λ — minimum 0; maximum 100
- Exact event count k — minimum 0; maximum 1000
Worked example
| Input | Value |
|---|---|
| Average event rate λ | 3 |
| Exact event count k | 2 |
P(X=2)≈0.2240.
Assumptions and limits
- The rate is nonnegative and events are modeled as independent counts with a constant average rate.
- The requested count is a nonnegative whole number.
- Time-varying rates, dependence, overdispersion, exposure conversion, and decisions are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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