3. Suppose that X and Y are two independent random variables (P(X = a, Y = b) = P(X = a)P(Y = b) for any a, b) and X - Binom(n, p) and Y Binom(m, p). Compute the probability ~ P(X + Y = k) and show that X + Y has a binomial distribution with parameters n + m and p. (Hint: Use (+)-(6)(7)+(6)(-1)+-+(C)(3)- T 0