TITLE: How many random samples needed to pick all elements of set?
QUESTION [7 upvotes]: If repeatedly picking a random element from a set, what is the expected number of times I'd have to pick before seeing all the elements of the set?
Edit: when picking an element, it is simply counted and not removed from the set, so it can be picked again.

REPLY [10 votes]: This is the coupon collector's problem.  The expected number of picks required to choose all the elements of the set is $$nH_n = n\sum_{i=1}^n\frac1i.$$