4. Consider a collection of N objects of which N1 are of type 1 and N; are of type 2. We select 71 objects from the collection of N at random and without replacement. Then the probability that exactly a: (where :c S. n, :c 5 N1 and n a: 5 N2) of these a objects are oftypelandnzrareoftypeZis (N') N\") ('3) i where N = N1+ N2 (a) Provide a brief argument for the above formula of the probability. (b) We say a discrete random variable is hyperyeometrically distributed if it has PMF (T) (i) (if) ' where z 5 n, a: 5 N1 and n a: 3' N2. Use the Vandermonde identity ("1:\") :(T) (it) to justify that px is a PMF. le-Tl =