Let X be a random variable such that X ∼ h(n;

a, b). Show that the probability function f of X can be calculated via the following recursive scheme:

f(x + 1) = (n-x)(a-x) (x+1)(bn+x+1) with the initial conditions f(x), max (0,n-b]x min{a, n}, and f(0)= f(n-b)= (h) (a+b) (nab) (a + b) n if n < b, if n b.