I don't even know how to begin this question. I'm not looking for a complete solution per se but I don't even know where to begin.

Suppose that X is a binomial random variable with parameters (m, θ) and Y is another

binomial random variable with parameters (n, θ) and suppose that X and Y are independent.

Let Z = X+Y . Show that Z is another Binomial random variable with parameters (m+n, θ).

Hint:

P

Note that you have to find the PMF of Z: P(Z = z). You may use the fact that

sum over k of (n choose k)(n choose (z-k) = (m plus n) choose z where the sum ranges over k for which the binomial coefficients are

defined.