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Show that if two binomial random variables X ∼ Bin(a,p) and Y ∼ Bin(b,p) are independent,...

Show that if two binomial random variables X ∼ Bin(a,p) and Y ∼ Bin(b,p) are independent, then X + Y ∼ Bin(a + b, p), using the technique of moment generating function.

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