Timeline for Probability of at least two of $n$ independent events occurring subject to some conditions
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 6, 2020 at 17:29 | vote | accept | Melika | ||
| Nov 7, 2018 at 19:37 | comment | added | Melika | @MattF That would be very great if you can share your solution with us. | |
| Nov 6, 2018 at 14:05 | comment | added | user44143 | @Melika I can write up that part | |
| Nov 6, 2018 at 11:22 | comment | added | Taro Tokyo | @Melika: Do you want the tight lower bound ? | |
| Nov 6, 2018 at 11:15 | comment | added | Taro Tokyo | @MattF: But I still did not see how can you prove that it is a 'good lower bound' for our probability. So, is it a 'good' lower bound or a 'possible' lower bound? | |
| Nov 6, 2018 at 1:37 | comment | added | Melika | My question is about this part of your claim: "...and a lower bound for all higher n if there are at most two distinct probabilities." How do you show this? | |
| Nov 5, 2018 at 18:02 | comment | added | user44143 | @TaroNGUYEN, it’s a lower bound for the exact results in the case n=3, a lower bound for all of the n=4 cases in which at least two probabilities agree (so at most three distinct probabilities), and a lower bound for all higher n if there are at most two distinct probabilities. I used the same formula for Fn as in your answer. | |
| Nov 3, 2018 at 19:10 | comment | added | Melika | I'm writing a computer science paper, and if I find a better lower-bound for this problem, it improves my result. I don't need a tight bound. What I have done by now is merely dividing them into two partitions $P_1$ and $P_2$ where $|\sum_{x\in P_1} \Pr[ x=1] - \sum_{x\in P2} \Pr[x=1]| \leq p/3$ and I've computed the probability that at least one of the variables in each partition is $1$. | |
| Nov 3, 2018 at 13:14 | comment | added | Taro Tokyo | Can you clarify your statement that it's a lower bound? | |
| Nov 3, 2018 at 7:05 | history | edited | user44143 | CC BY-SA 4.0 |
corrected denominator in first expression
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| Nov 3, 2018 at 6:38 | comment | added | user44143 | I have ideas for a proof, but haven’t explored them in detail. Can you say more about your motivation or the context for the question? | |
| Nov 2, 2018 at 8:24 | comment | added | Melika | Thanks a lot. Do you have a proof for the mentioned lower-bound? I would very much appreciate if you could provide the proof since this is a very interesting bound and is exactly what I need. | |
| Nov 1, 2018 at 14:43 | history | edited | user44143 | CC BY-SA 4.0 |
added limit analysis and graph
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| Nov 1, 2018 at 14:01 | history | edited | user44143 | CC BY-SA 4.0 |
better notation
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| Nov 1, 2018 at 10:45 | history | edited | user44143 | CC BY-SA 4.0 |
estimated both transitions
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| Nov 1, 2018 at 10:33 | history | edited | user44143 | CC BY-SA 4.0 |
added conjectures for large n
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| Nov 1, 2018 at 8:58 | history | edited | user44143 | CC BY-SA 4.0 |
added 8 characters in body
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| Nov 1, 2018 at 8:19 | history | edited | user44143 | CC BY-SA 4.0 |
added 2 characters in body
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| Nov 1, 2018 at 8:07 | history | edited | user44143 | CC BY-SA 4.0 |
added code
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| Nov 1, 2018 at 7:52 | history | answered | user44143 | CC BY-SA 4.0 |