4. Consider a collection of N objects of which N are of type 1 and N2 are of type 2. We select n objects from the collection of N at random and without replacement. Then the probability that exactly x (where x n, x N and n-x 2) of these n objects are of type 1 and n-x are of type 2 is where N N + N (M) (N) (M) (a) Provide a brief argument for the above formula of the probability. (b) We say a discrete random variable is hypergeometrically distributed if it has PMF N2 Px(x) = () (2) (N) where xn, x N and n-x 2. Use the Vandermonde identity (m + n). m n = to justify that px is a PMF.