VastCalc
Statistics
Poisson Distribution Calculator
Calculate Poisson probabilities P(X = k), P(X ≤ k), and P(X ≥ k) for a given average rate of occurrence (lambda).

Poisson Distribution Calculator

Calculate Poisson probabilities for events that occur at a known average rate. Enter the average rate (lambda) and desired number of events to find exact and cumulative probabilities.

The Poisson distribution models the probability of a number of events occurring in a fixed interval when events happen at a constant average rate independently.

PMF: P(X = k) = (λ^k × e^(-λ)) / k!

Key Properties:

  • Mean = λ
  • Variance = λ
  • Standard deviation = √λ

Common Applications:

  • Calls to a call center per hour
  • Website visits per minute
  • Defects per unit of product
  • Accidents per month

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