probability - Counting Couples - Mathematics

N ow introduce summing the recurrence relations we

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Unformatted text preview: epresents the number of couples. N ow introduce Summing the recurrence relations, we find and similarly Solving this system of equations, we obtain so that N ow observe that ma th.sta c ke xc ha nge .c om/que stions/336896/c ounting- c ouple s 2/4 3/27/13 pr oba bility - Counting Couple s - Ma the ma tic s a nd This is a nice sanity check, a kind of hash certificate that shows that we have the right generating function. To conclude note that so that It follows that the expected number of couples is I do believe that this is a nice exercise in the use of ordinary generating functions including the sanity check (obviously the number of arrangements is choose .) With these generating functions we can calculate arbitrary factorial moments of a nsw ered Ma r 21 a t 23:52 Ma rko Riedel 1,079 1 2 10 Continuing the computation we can calculate . We have After a straightforward calculation this transforms into a nsw ered Ma r 22 a t 0:29 Ma rko Riedel 1,079 1 2 10 ma th.sta c ke xc ha nge .c om/que stions/336896/c ounting- c ouple s 3/4 3/27/13 ma th.sta c ke xc ha nge .c om/que stions/336896/c ounting- c ouple s pr oba bility - Counting Couple s - Ma the ma tic s 4/4...
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This document was uploaded on 02/23/2014 for the course CS 214 at Rutgers.

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