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Poisson Process Calculator

Calculate probabilities and distributions for homogeneous Poisson processes including increment probabilities, event occurrence times, and time intervals.

Homogeneous Poisson Process Calculator
Calculate probabilities and distributions for Poisson processes with constant intensity

The average rate of events occurring per unit time

Number of events in the time interval (s, t]

About Poisson Processes

Key Properties:

  • • Independent Increments: Events in non-overlapping time intervals are independent
  • • Stationary Increments: Probability distribution depends only on time interval length
  • • Rare Events: Multiple events rarely occur simultaneously

Applications:

  • • Customer arrivals at service systems
  • • Radioactive decay events
  • • Traffic flow and accidents
  • • Communication network packets
Calculation Results
Results for Increment Probability calculation

Enter parameters and click Calculate to see results

Related Resources
Learn Poisson Processes
Comprehensive theory and examples
Practice Problems
Test your understanding with exercises
Formula Reference
Key formulas and properties