Poisson equations

· Format:

Poisson(λt)

· Probability mass function:

$\begin{array}{l}\displaystyle f(x)=\frac{e^{-\lambda t} \big(\lambda t \big)^{x}}{x!}\end{array}$

· Cumulative distribution function:

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

· 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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