Question
  1. Let X­­1 ~ Binomial(n1p), and let X2 ~ Binomial(n2p), independent of X1.  Show using a discrete transformation that Y = X1 + X2 ~ Binomial(n1 + n2, p).  Explain why this result makes sense intuitively.  Hint: the hypergeometric distribution may be helpful in finding the final marginal p.m.f.

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