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**Answer**

** Poisson Distribution Mean**

The Mean can be derived from the MGF of Poisson Distribution.

The MGF of Poisson Distribution is; $={e}^{\lambda ({e}^{t}-1)}$

$Mean\left(x\right)={M}_{X}^{I}\left(0\right)$

${M}_{x}^{I}\left(t\right)=\lambda {e}^{t}*{e}^{\lambda ({e}^{t}-1)}$

Replacing the value of t with zero (0)

We have;

${M}_{x}^{I}\left(0\right)=\lambda {e}^{0}*{e}^{\lambda ({e}^{0}-1)}$

${M}_{x}^{I}\left(t\right)=\lambda $

The **Mean of Poisson Distribution** is $\lambda $

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