Poisson Distribution Calculator

Calculate probabilities for events occurring randomly over a fixed interval using the Poisson distribution.

Distribution Parameters

Calculation Type

Poisson Distribution Formula

The probability mass function of the Poisson distribution is:

P(X=k)=e−λλkk!P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}

Where:

  • λ\lambda = Average rate of events per interval
  • kk = Number of events
  • ee = Euler's number (approximately 2.71828)
  • k!k! = Factorial of k

Distribution Properties

Mean (μ): λ = 5

Variance (σ²): λ = 5

Standard Deviation (σ): √λ = 2.23606797749979

Poisson Distribution Visualization

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