Timeline for Probability of a sum of random variables falling in a given range
Current License: CC BY-SA 4.0
22 events
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| Feb 28, 2022 at 17:28 | comment | added | whuber♦ | That's a little too broad for our format. This is a difficult area of probability theory: you describe a form of random walk with an absorbing barrier at $a.$ A great deal has been written about just the cases where $P$ is a binomial distribution or is a Normal distribution. What you ask, then, looks like it would be an extensive treatise. stats.stackexchange.com/questions/145621 is an example of just one very special case of this situation. | |
| Feb 28, 2022 at 16:56 | history | edited | alexmolas | CC BY-SA 4.0 |
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| Feb 28, 2022 at 16:39 | history | edited | alexmolas | CC BY-SA 4.0 |
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| Feb 28, 2022 at 16:38 | comment | added | alexmolas | I would like to keep the answer as general as possible. I don't want to fix the details of $P$, but have an answer that depends on $P$, $a$, and $b$. Does it make sense? | |
| Feb 28, 2022 at 16:13 | comment | added | whuber♦ | Although after the edit I have voted to reopen this question, it has a fundamental problem: the answer, and how one goes about getting an answer, depends on the details of the distribution $P.$ What can you tell us about this distribution in the situation you actually face? | |
| Feb 28, 2022 at 16:12 | history | reopened |
Adrian Keister whuber♦ |
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| Feb 28, 2022 at 14:50 | comment | added | alexmolas | @Glen_b thank you for your feedback. I've just edited the question with some examples and a more formal definition of the problem. Let me know if now it's clear :) | |
| S Feb 28, 2022 at 14:49 | review | Reopen votes | |||
| Feb 28, 2022 at 16:18 | |||||
| S Feb 28, 2022 at 14:49 | history | edited | alexmolas | CC BY-SA 4.0 |
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| Feb 28, 2022 at 13:35 | comment | added | whuber♦ | alexm, I believe I see what you're trying to ask. There's potential for confusion, though, because you use $b$ in a context where it's unneeded. The process stops when $x\ge a,$ period, regardless of what $b$ might be. However, after the process has stopped, you check whether $x\le b.$ I think if you were to clear that up in your post (assuming this is a correct interpretation), it would quickly be reopened. You also need to specify that $P$ won't produce many negative numbers (having a positive expected value would suffice), for otherwise the process might never stop! | |
| Feb 28, 2022 at 2:45 | history | closed |
Glen_b kjetil b halvorsen♦ |
Needs details or clarity | |
| Feb 27, 2022 at 23:11 | review | Close votes | |||
| Feb 28, 2022 at 2:45 | |||||
| Feb 27, 2022 at 21:48 | history | edited | alexmolas | CC BY-SA 4.0 |
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| Feb 27, 2022 at 21:42 | history | edited | alexmolas | CC BY-SA 4.0 |
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| Feb 27, 2022 at 21:36 | comment | added | alexmolas | @StratosFair no, it is any distribution. | |
| Feb 27, 2022 at 21:31 | comment | added | Stratos supports the strike | Is $P$ the uniform distribution on $(a,b)$ ? | |
| Feb 27, 2022 at 21:27 | comment | added | kjetil b halvorsen♦ | That last part ut without wanting to get a value higher than 𝑏 is nowwhere in your Q! Please read it again, and edit ... | |
| Feb 27, 2022 at 21:21 | comment | added | alexmolas | Why? I don't understand why it's not clear in the original description. The idea is to add up numbers until you get a number higher than $a$ but without wanting to get a value higher than $b$. | |
| Feb 27, 2022 at 21:12 | comment | added | kjetil b halvorsen♦ | Then you need to revise your description, which must be incomplete! | |
| Feb 27, 2022 at 21:09 | comment | added | alexmolas | Yes it plays a role, if $b=a$ then the probability is 0, but if $b=\infty$ then the probability is 1. | |
| S Feb 27, 2022 at 20:49 | review | First questions | |||
| Feb 27, 2022 at 21:00 | |||||
| S Feb 27, 2022 at 20:49 | history | asked | alexmolas | CC BY-SA 4.0 |