Question: 1.3.8 Let X and Y be independent binomial random variables having parameters .N;p/ and .M;p/, respectively. Let Z D X CY. (a) Argue that Z

1.3.8 Let X and Y be independent binomial random variables having parameters

.N;p/ and .M;p/, respectively. Let Z D X CY.

(a) Argue that Z has a binomial distribution with parameters .N CM;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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