In Problem 9, compute the variance of the number of empty urns. Problem 9 A total of

Question:

In Problem 9, compute the variance of the number of empty urns.
Problem 9
A total of n balls, numbered 1 through n, are put into n urns, also numbered 1 through n in such a way that ball i is equally likely to go into any of the urns 1, 2, . . . , i. Find
(a) The expected number of urns that are empty;
(b) The probability that none of the urns is empty.