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·       Format:

Poisson(λt)

·       Probability mass function:

f(x)=\frac{e^{-\lambda t} \big(\lambda t \big)^{x}}{x!}

·       Cumulative distribution function:

F(x)=e^{-\lambda t} \displaystyle\sum_{i=0}^{\lfloor x \rfloor}\frac{\big(\lambda t\big)^{i}}{i!}

·       Parameter restrictions:

λt > 0

·       Domain: 

x = {0,1,2,...}

·       Mean:

λt

·       Mode: 

λt, λt -1       if λt is an integer

|λt|             otherwise

·       Variance:

λt

 


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