statistics

Mean of poisson distribution

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The_Don. answered · 13/06/2021

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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; $= e^{λ (e^{t} - 1)}$

$M e a n (x) = M_{X}^{I} (0)$

$M_{x}^{I} (t) = λ e^{t} * e^{λ (e^{t} - 1)}$

Replacing the value of t with zero (0)

We have;

$M_{x}^{I} (0) = λ e^{0} * e^{λ (e^{0} - 1)}$

$M_{x}^{I} (t) = λ$

The Mean of Poisson Distribution is $λ$

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