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October 1st, 2012, 04:16 PM   #1
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Expectation of picking all N numbers from N distinct numbers

Hi all, I've just gotten into a problem.

There are N distinct numbers, say, 1, ..., 100. One wants to pick up all of them with replacement. My task is to compute the mathematical expactation of how many times s/he needs to pick up all 100 distinct number.

I think it's kind of difficult since I've to compute the probabilites of 100 times to get all numbers, 101 times to get all number, ..., so on so forth. It's kind of intractable.

Any ideas on this problem? Thanks!!
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October 1st, 2012, 05:14 PM   #2
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Re: Expectation of picking all N numbers from N distinct num

Hi all,

I got the prototype of the problem. It's named "coupon collector's problem".

http://en.wikipedia.org/wiki/Coupon_col ... 7s_problem
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