Question: 3.8. Let X and Y be independent binomial random variables having parameters (N, p) and (M, p), respectively. Let Z = X + Y. (a)

3.8. Let X and Y be independent binomial random variables having parameters

(N, p) and (M, p), respectively. Let Z = X + Y.

(a) Argue that Z has a binomial distribution with parameters (N + M, p)

by writing X and Y as appropriate sums of Bernoulli random variables.

(b) Validate the result in

(a) by evaluating the necessary convolution.

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