# PGF for Poisson Distribution.

• A
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?

Last edited:

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

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

Dale
Gold Member
Forum rules do not view it that way

Okay. I accept.

Gold Member
Forum rules do not view it that way

Where can/should I post these kinds of problems?

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.