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Recently I tried to solve a problem that based on coupons collector problem. Let it be sth like this:

If a package has one of 50 random baseball cards, how many packages do you need to buy to get a complete set? (or sth like this, doesnt matter)

If I need every card one time, so it makes one set that is easy, explaination is on wikipedia and I already understood it. But what if we consider to collect every card k times? (To collect k sets of cards)

How can I tried to solve this problem? I found sth about Chernoff's bound (http://www.math.ucla.edu/~pak/courses/pg/l10.pdf) but I dont get it actually if it is a solution of this problem. I need to estimate E(X) and Var(X) for k sets of cards.

Could anyone give me a hint how to solve this problem? Thanks for all answers:)

Greetings,

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    The answer is on the Wikipedia page on the Coupon Collector's problem: http://en.wikipedia.org/wiki/Coupon_collector%27s_problem#Extensions_and_generalizations , where the Newman-Shepp result says that approximately $\Theta(n\log\log n)$ more samples are needed for each additional set. You should be able to find their AMM article without too much trouble.2012-05-29
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    @StevenStadnicki the Wikipedia link gives $O(n \log n)$ not $O(n \log \log n)$ (unless we think of $k$ as a function of $n$...).2012-05-29
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    @JohnEngbers Wikipedia says $n\log n+(k-1)n\log\log n$, so I was breaking it down as $n\log n$ for the 'first' (which was the result I presumed the OP already knew) and then $n\log\log n$ for each additional set.2012-05-30

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