A PGF for Poisson Distribution.

user366312

Gold Member
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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Periwinkle

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

StoneTemplePython

Gold Member
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

Gold Member

user366312

Gold Member
Forum rules do not view it that way
Where can/should I post these kinds of problems?

Gold Member

berkeman

Mentor
I am not doing homework. I am preparing for a test. I believe there are differences between these two.
Okay. I accept.
Thank you. You will get great help in the schoolwork forums on your questions, as long as you show your efforts.

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