A PGF for Poisson Distribution.

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user366312

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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?
 
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Encyclopedia of Mathematics describes Poisson distribution characteristics according to which you are right.
 

user366312

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StoneTemplePython

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I am not doing homework. I am preparing for a test. I believe there are differences between these two.
Forum rules do not view it that way
 

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