Poisson Distribution

Pocket

By using \lambda as a parameter, the Poisson distribution is defined as follows:

f(k)=P(X=k)=\frac{\lambda^ke^{-\lambda}}{k!}

 

The expectation value and variance of Poisson distribution can be computed as follows:

E[X]=\int_{-\infty}^\infty kf(k) dk = \lambda

 

V[X]=\int_{-\infty}^\infty (k-E[X])^2f(k) dk = \lambda

 

The Generating function of the Poisson distribution can be evaluated as follows:

G[x]=\sum_{k=0}^\infty f(k)x^k=e^{\lambda(x-1)}

 

 

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