19. Let X denote a hypergeometric random variable with parameters n, m, and k. That is,

(0)(2) m P{X=i}=- n+m i=0,1,..., min(k,n) a. Derive a formula for P{X=i} in terms of P{X = i-1}. b. Use part (a) to compute P{X=i) for i = 0, 1, 2, 3, 4, 5 when n=m= 10, k = 5, by starting with P{X=0}. c. Based on the recursion in part (a), write a program to compute the hypergeometric distribution function. d. Use your program from part (c) to compute P{X < 10} when n = m = 30, k = 15.