Question: Using MGFs prove that if X Binomial(m, p) and Y Binomial(n, p) are independent, then X + Y Binomial(m + n, p).

Using MGFs prove that if X ∼ Binomial(m, p) and Y ∼ Binomial(n, p) are independent, then X + Y ∼ Binomial(m + n, p).

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