Timeline for Probability of having a bounded ratio of two types of balls in each of 'S' bins after random partitioning of a fixed number of balls
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2011 at 15:30 | vote | accept | user14324 | ||
| Apr 23, 2011 at 11:39 | answer | added | Douglas Zare | timeline score: 4 | |
| Apr 22, 2011 at 18:38 | history | edited | user14324 | CC BY-SA 3.0 |
Replaced the mushroom story with a more appropriate example; deleted 6 characters in body; added 36 characters in body; Post Made Community Wiki
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| Apr 22, 2011 at 16:02 | history | edited | user14324 | CC BY-SA 3.0 |
added 83 characters in body
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| Apr 22, 2011 at 15:55 | history | edited | user14324 | CC BY-SA 3.0 |
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| Apr 22, 2011 at 15:01 | comment | added | Andrew D. King | I agree with Peter. For certain values of $S$, $L$, and $A$, the Chernoff bound seems like it would be more than sufficient. | |
| Apr 22, 2011 at 11:47 | comment | added | Peter Shor | It would help if we knew the relative sizes (or even approximate orders of magnitude) of $A$, $B$, $S$. Are you interested in the limit where $S$ goes to $\infty$ and $L$ is fixed size, or do you want $L$ to grow with $S$, or are you interested in the case where they are all around $10^3$, or ...? | |
| Apr 21, 2011 at 19:45 | history | edited | user14324 | CC BY-SA 3.0 |
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| Apr 21, 2011 at 3:54 | comment | added | Douglas Zare | I don't think the poison mushroom description helps. Does "industrial waste buried in the field leeching a toxin with an extremely sharp dose-response curve" reach anyone who couldn't read the abstract version? | |
| Apr 21, 2011 at 2:06 | comment | added | Thomas Kalinowski | Let $P$ be the set of all (ordered) partitions $B=b_1+\cdots+b_S$ with $0\leqslant b_i\leqslant k$. Then your probability should be something like [\frac{\sum_{(b_1,\ldots,b_S)\in P}\binom{L}{b_1}\binom{L}{b_2}\cdots\binom{L}{b_S}}{\binom{N}{B}},] but that's probably not the type of answer you are looking for. | |
| Apr 20, 2011 at 22:28 | history | edited | user14324 | CC BY-SA 3.0 |
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| Apr 20, 2011 at 21:43 | comment | added | user14324 | Folks, you're absolutely right, I need to fix this question... hang tight. | |
| Apr 20, 2011 at 6:05 | comment | added | user11235 | "Evenness" constraint is really a very misleading description. | |
| Apr 19, 2011 at 21:57 | comment | added | user14324 | Dear Nick, you're right... sorry I wrote this on my phone. I rephrased the question and hopefully made it more straightforward. | |
| Apr 19, 2011 at 21:56 | history | edited | user14324 | CC BY-SA 3.0 |
Rephrased the question to make it clearer
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| Apr 19, 2011 at 21:36 | comment | added | Nick Loughlin | Perhaps you mean to ask the probability of there being two fixed values each in $[0,1]$ such that the ratio in each bin of blue balls to red balls is bounded between them? My apologies, but the wording of your question seems ambiguous to me, or at least unclear. | |
| Apr 19, 2011 at 20:53 | history | edited | user14324 | CC BY-SA 3.0 |
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| Apr 19, 2011 at 20:47 | history | asked | user14324 | CC BY-SA 3.0 |