please please help me out for these question below. They are very important to me. As I am not good on Statistic and I don't have the model answers for them, I really want someone who can show me the answers about them. Therefore, I can check if i was doing the questions in the right way.

Thank you very much!!!

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Question 3---Let X and Y be random variables all of whose values are non-negative integers.

(a) Define the probability generating function of X.

(b) State a theorem linking the probability generating functions of X, Y and X+Y in the case that X and Y are independent of each other.

(c) Suppose that X~Poisson(入). Find the probability generating function of X.

(d) Suppose that X and Y are independent of each other, X ~Poisson(入) and

Y~Poisson(入). Find the distribution of X + Y .

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