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August 15th, 2007, 04:49 AM  #1 
Newbie Joined: Aug 2007 Posts: 3 Thanks: 0  bins and balls  uniform random selection problem
I have N bins and n balls, N >> n (eg. if N = 100, n = 5). For every bin N_i (i = 0..N1) I choose uniformly and randomly q balls n_i (i = 0..n1), q < n (eg. q = 3). I "copy" the chosen balls into the bin, and move to the next bin, where I again randomly select q balls from the initial set of balls and copy them into the bin, etc. for all bins. In the end each bin contains exactly q balls, copied randomly from the initial set of n balls. How can I calculate statistically in how many bins N_i (i = 0..N1), each ball n_i (i =0..n1) was copied? Thanks! 
August 15th, 2007, 04:45 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717 
It looks to me like a binomial distribution. Prob (P) a given ball is in a given bin is q/n. Prob (Q) is not is 1P. Expand (P+Q)^N. First term (P^N) is prob. a ball is in all bins, last term (Q^N) is prob. ball in no bins. Mean no. bins is NP. 
August 16th, 2007, 12:35 AM  #3  
Newbie Joined: Aug 2007 Posts: 3 Thanks: 0 
Thanks for your reply, mathman! Quote:
Quote:
Thanks!  
August 16th, 2007, 01:40 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  Quote:
Quote:
Quote:
 
August 17th, 2007, 07:24 AM  #5 
Newbie Joined: Aug 2007 Posts: 3 Thanks: 0  Thanks
I got it! Thanks!


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