1.3.8 Let X and Y be independent binomial random variables having parameters (N, p) and (M,p), respectively. Let Z=X+Y. An Introduction to Stochastic Modeling (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. (3 %)*(1 – p)N-*()***(1 – p)=n+ Osnsm e(n)=f"(1 – p)***Ë (^)(-_^) N-k M (n) = { * M +1
