16. Suppose that balls are randomly removed from an urn initially containing n white and m black balls. It was shown in Example 2m that E[X] =

1 + m/(n + 1), when X is the number of draws needed to obtain a white ball.

(a) Compute Var(X).

(b) Show that the expected number of balls that need be drawn to amass a total of k white balls is k[1 + m/(n + 1)].

HINT: Let Y_i, i = 1, ..., n + 1, denote the number of black balls withdrawn after the (i)st white ball and before the (i + 1)st white ball. Argue that the Y_i, i = 1, ..., n + 1, are identically distributed.