#### user366312

Gold Member

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Can anyone kindly tell me how I can derive a Probability Generating Function of Poisson Distribution for ##X+Y## where ##X## and ##Y## are independent?

I know that PGF for a single variate Poisson Distribution is: ##G(t) = e^{-\lambda (1-t)}##.

Then how can I derive a PGF for the same?

Is it: ##G(t) = e^{-(\lambda_X + \lambda_Y)(1-t)}## ?

Why or why not?

I know that PGF for a single variate Poisson Distribution is: ##G(t) = e^{-\lambda (1-t)}##.

Then how can I derive a PGF for the same?

Is it: ##G(t) = e^{-(\lambda_X + \lambda_Y)(1-t)}## ?

Why or why not?

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