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December 14th, 2010, 02:04 AM  #1 
Newbie Joined: Dec 2010 Posts: 4 Thanks: 0  Number of unique after n samples
Consider an urn containing B balls. What is the expression for the expected number of unique balls drawn after n samples, if sampling is independent and with replacement? This one has me stumped, even though it appears simple. Can anyone on here crack it? Regards, BigBugBuzz 
December 14th, 2010, 01:09 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,823 Thanks: 723  Re: Number of unique after n samples
The question is a little unclear. Are the balls all the same or are they marked different? Does unique mean not picking a ball after it has already been picked and put back?

December 15th, 2010, 02:56 AM  #3  
Newbie Joined: Dec 2010 Posts: 4 Thanks: 0  Re: Number of unique after n samples Quote:
Let's say the balls have an ID form 1 to B. As an example of number of unique, consider that n = 3 and that the following ID's were drawn 3, 5, 5. Here the number of unique is 2, because the ID of 5 was drawn twice, but should only be counted once. There is noting that prevents an ID being part of a given sample many times (because sampling is done with replacement), but it is of course unlikely for large values of B. I hope this helps.  
December 15th, 2010, 01:25 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,823 Thanks: 723  Re: Number of unique after n samples
You are dealing with a multinomial distribution. I suggest you look it up (google  Wikipedia, etc.).


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