# 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.

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.

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