Deriving a Probability Generating Function for Independent Poisson Variables

[user366312]

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?

 

[Periwinkle]

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

 

[StoneTemplePython]

It was a recent homework thread, here:
https://www.physicsforums.com/threads/need-help-simplifying-a-summation-with-binomials.958233/

For that matter, your posts are looking a lot like homework problems.

 

[user366312]

It was a recent homework thread, here:
https://www.physicsforums.com/threads/need-help-simplifying-a-summation-with-binomials.958233/

For that matter, your posts are looking a lot like homework problems.

I am not doing homework. I am preparing for a test. I believe there are differences between these two.

 

[StoneTemplePython]

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

 

[user366312]

Forum rules do not view it that way

Okay. I accept.

 

[user366312]

Forum rules do not view it that way

Where can/should I post these kinds of problems?

 

[StoneTemplePython]

Where can/should I post these kinds of problems?

Calculus forum, using the template.

If you want an outside resource to use, you may find

http://www.randomservices.org/random/poisson/index.html
to be helpful

 

[berkeman]

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.