What Is the Poisson Distribution Probability Calculator?
A Poisson distribution probability calculator determines likelihood of discrete counts occurring over time or spatial areas.
How Does the Poisson Distribution Probability Calculator Work?
Evaluates the discrete probability mass function (PMF) and sums sequential steps for cumulative distribution (CDF).
Poisson Distribution Probability Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
P(X = k) = (λᵏ × e⁻ᵞ) ÷ k!
Multiplies average rate raised to k by e raised to negative lambda, divided by the factorial of k.
How to Use the Poisson Distribution Probability Calculator
- Input the average historical occurrence rate λ and your query event count k.
Step-by-Step Example Calculation
Average rate λ = 3 with target k = 2
Input Values:
lambda:3
k:2
Understanding Your Result
Displays exact point probability, cumulative probability of at most k events, and tail probability of more than k events.
Factors That Affect the Result
- Mean event rate λ dictates the center and spread of the distribution.
When Should You Use This Calculator?
- Call center queue modeling, website server request provisioning, hospital ER admissions, and defect rate inspections.
Assumptions & Limitations
- Events must occur independently and at a constant continuous rate.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Siméon Denis Poisson formulation evaluated with exact factorial expansion.