Question: Let X and Y be two independent random variables, both from Poisson distribution with the same parameter t : (a) Use moment generating functions to

Let X and Y be two independent random variables, both from Poisson distribution with the same parameter t :

(a) Use moment generating functions to prove that the sum X+Y also has a Poisson distribution. Identify the parameter of the distribution.

(b) Does 2X also have a Poisson distribution? Justify your answer!

(c) Does 1/2 X also have a Poisson distribution? Justify your answer

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