Suppose X and Y are independent with the following binomial distributions: X Binom(n, p) and Y

Question:

Suppose X and Y are independent with the following binomial distributions: X ∼ Binom(n, p) and Y ∼ Binom(m, p). Show that X + Y has a binomial distribution and give the parameters. (Use Equation 3.13.)

Equation 3.13.

Cov(X, Y) = E[(X − μX)(Y − μY)].

Distribution
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