let X1binomialn1 p and X2binomialn2p independent of X1 Show

let X₁~binomial(n₁ ,p), and X₂~binomial(n₂,p), independent of X₁. Show using a decreate transformation the 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.

Solution