In Problem 1, compute the variance of the number of empty urns.
Problem 1
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.
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