Question

Show that the skewness of X~Poisson(λ) is λ^-(1/2)

Answer 1

Let X is Poisson variable with parameter . PDF of Poisson distribution is

MGF of X will be

So MGF of Poisson distribution is

Differentiating above with respect to t gives:

So putting t=0 gives

Differentiating MGF again with respect to t gives:

So putting t=0 gives

Therefore variance will be

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Differentiating MGF again with respect to t gives:

So putting t=0 gives

So third central moment is

Skewness:

Hence, proved