Timeline for Why do we need random variables?
Current License: CC BY-SA 3.0
52 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Oct 24, 2016 at 18:37 | comment | added | Filippo Alberto Edoardo | @Olivier: Thanks, I've downloaded it. It might somehow contain a very good alternative approach to my question which might turn our to be even more interesting ;) | |
| Oct 22, 2016 at 7:34 | comment | added | Olivier | Now that you're a pro in probability :-) , you may enjoy reading this paper: "On random variables - without basic space" math.uni-frankfurt.de/~ismi/kersting/research/RandVar.pdf It takes the exact "contrepied" to your question: could we do without an underlying sample space? | |
| Oct 19, 2016 at 16:29 | answer | added | Vamsi | timeline score: 3 | |
| Oct 19, 2016 at 14:18 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
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| Oct 19, 2016 at 14:17 | vote | accept | Filippo Alberto Edoardo | ||
| Oct 18, 2016 at 23:38 | answer | added | P Vanchinathan | timeline score: 20 | |
| Oct 18, 2016 at 20:56 | answer | added | Rogier Brussee | timeline score: 4 | |
| Sep 28, 2016 at 19:15 | comment | added | reuns | In signal processing (and in machine learning) we often replace the probabilistic models (random variables, maximum likelihood for estimating the parameters) by some explicit minimization criterion (without any specified model for the data). In general the maths are much easier in the minimization/analytic world (where the equation are explicit), but the intuition is much easier in the probabilistic world (where the model that we assume for the data is explicit). | |
| Sep 28, 2016 at 8:15 | comment | added | Filippo Alberto Edoardo | Thank you, indeed I was a bit perplex from the harsh reactions. It seems anyhow that after a first small list of violent comments, the situation got better and many people offered valuable answers or insights. | |
| Sep 28, 2016 at 2:44 | comment | added | Gerry Myerson | Before anyone else votes to close, let me note that questions on how to teach advanced undergraduate subjects have generally been considered on-topic here, even though strictly speaking they don't concern mathematical research. They concern things that research mathematicians frequently do, and that people other than research mathematicians do less frequently if at all, and as such they have been tolerated here. | |
| Sep 28, 2016 at 2:40 | history | edited | Gerry Myerson |
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| Sep 28, 2016 at 1:17 | answer | added | Iosif Pinelis | timeline score: 6 | |
| Sep 25, 2016 at 14:32 | answer | added | Joe Silverman | timeline score: 14 | |
| Sep 25, 2016 at 14:18 | comment | added | fedja | @wolfies Apparently the Universe just needs some kind of eyes to look into the mirror. But why She developed such strange ones, I cannot answer :-) | |
| Sep 25, 2016 at 13:57 | answer | added | Steven Landsburg | timeline score: 7 | |
| Sep 25, 2016 at 12:29 | answer | added | user13113 | timeline score: 6 | |
| Sep 24, 2016 at 17:21 | answer | added | user21820 | timeline score: 5 | |
| Sep 24, 2016 at 8:33 | comment | added | wolfies | More pertinently, why do random variables need us? | |
| Sep 23, 2016 at 21:11 | vote | accept | Filippo Alberto Edoardo | ||
| Oct 19, 2016 at 14:17 | |||||
| Sep 23, 2016 at 21:08 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
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| Sep 23, 2016 at 21:04 | comment | added | Filippo Alberto Edoardo | @GeraldEdgar I agree, but I hoped to get a bit of insight myself too instead of simply throwing out things I haven't digested yet... | |
| Sep 23, 2016 at 21:00 | comment | added | Douglas Zare | Despite the statement that this "had no success" on MSE, that question had two upvoted answers including one that was accepted, and fedja recently posted an answer there. math.stackexchange.com/questions/123186/… | |
| Sep 23, 2016 at 20:50 | review | Close votes | |||
| Sep 24, 2016 at 2:51 | |||||
| Sep 23, 2016 at 20:48 | comment | added | Gerald Edgar | For first-time teacher of the subject, my advice is: Find a good textbook, and follow it. Experienced instructors (who may write such a textbook after years of experience teaching it) understand how to do these things. In particular, "random variables" should not be at the beginning of the course. Only much later. | |
| Sep 23, 2016 at 20:47 | comment | added | Douglas Zare | I feel that as the OP gets more of a background in probability, including understanding the material he should teach in a first college course on probability, he will understand many of the arguments given better. I don't find it valid or helpful to say that we don't need random variables because we could just consider incredibly complicated events on a product of spaces instead of talking about linearity of expectation. That seems like saying we don't need number fields in Galois theory because we could make convoluted statements about $\mathbb{Z}$ instead. | |
| Sep 23, 2016 at 20:35 | comment | added | BlueRaja | This question now on the "hot questions" list - why is it even still open!? | |
| Sep 23, 2016 at 17:36 | answer | added | Dirk | timeline score: 2 | |
| Sep 23, 2016 at 16:43 | answer | added | Nawaf Bou-Rabee | timeline score: 3 | |
| Sep 23, 2016 at 15:59 | comment | added | arsmath | I still don't understand this question. Literally everything in probability is a random variable. It's like asking "why do we need probability"? Every single statistic you would compute on a random sample is a random variable: the mean, the standard deviation, the median, the minimum, the maximum. | |
| Sep 23, 2016 at 15:38 | answer | added | Timothy Chow | timeline score: 13 | |
| Sep 23, 2016 at 9:07 | answer | added | user36212 | timeline score: 4 | |
| Sep 23, 2016 at 8:14 | answer | added | Michael Greinecker | timeline score: 40 | |
| Sep 23, 2016 at 7:26 | answer | added | მამუკა ჯიბლაძე | timeline score: 6 | |
| Sep 23, 2016 at 7:02 | answer | added | Robert Israel | timeline score: 17 | |
| Sep 23, 2016 at 6:30 | answer | added | Bjørn Kjos-Hanssen | timeline score: 12 | |
| Sep 23, 2016 at 5:47 | history | reopened |
Michael Greinecker R.P. Yemon Choi Alexey Ustinov Bjørn Kjos-Hanssen |
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| Sep 22, 2016 at 21:52 | review | Reopen votes | |||
| Sep 23, 2016 at 5:52 | |||||
| Sep 22, 2016 at 21:33 | comment | added | Filippo Alberto Edoardo | @MichaelGreinecker I have tried to make it a bit clearer, hoping that might help. | |
| Sep 22, 2016 at 21:32 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
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| Sep 22, 2016 at 20:59 | comment | added | Ryan Budney | A big difference between the random variable question and the ideals question is it appears to be that ideals are a rather technical tool required for a fairly limited context, where a random variable is more for the purpose of creating a context. Much like how topological spaces are here for a fairly soft purpose of holding together "nearness" arguments. | |
| Sep 22, 2016 at 20:37 | comment | added | Michael Greinecker | @FilippoAlbertoEdoardo It seems to me there might several quite different questions lurking there. There is the mathematical question of why one may not always just work with the distributions and forget underlying probability spaces. This question is answerable, even though most answers I can think of are outside the scope of a "basic probability" , which can mean a lot of things. There are also didactic questions, which are very different and greatly limit the scope of answers to the first question. | |
| Sep 22, 2016 at 20:34 | comment | added | Filippo Alberto Edoardo | ...of course, any help would be appreciated if you want to edit the question, which your reputation entitles you to, and to make it more understandable. | |
| Sep 22, 2016 at 20:32 | comment | added | Filippo Alberto Edoardo | @RyanBudney I agree that my question is vague (I might add a "soft question" tag). But if a mathematician willing to teach algebraic number theory—my domain—asked me "why do you need ideals", for instance, or "how to motivate the study of the structure of $\mathcal{O}_K^\times$ for a number field" I would propose something. I could give examples where working with elements is not enough (e.g. factorisation into primes) or where the knowledge of units gives you insight in other questions (principality of ideals), etc... And, honestly, I know no textbook in basic algebra adressing this question | |
| Sep 22, 2016 at 20:04 | comment | added | Ryan Budney | I think it's unclear what you might expect an answer to be. Do you have an answer to questions like "why do we need topology?" or "why do we need numbers?" There are of course many answers to these questions, from the pragmatic (applications) to answers more interior to mathematics. Most of these answers can be found by reading a basic textbook on the subject. I think people are confused because you don't appear to be addressing any of these concerns. | |
| Sep 22, 2016 at 18:43 | comment | added | Filippo Alberto Edoardo | I am very happy to close the question here, I simply did not put another one on stackexchange since it had no success there. Anyhow, the point is that I do not know what it is good for, and I am trying to ask the experts. I am not trying to criticise the introduction of random variables whatsoever, that would simply be ridiculous: I am wondering and hoping for some help. | |
| Sep 22, 2016 at 18:36 | comment | added | Douglas Zare | What is your substitute for the expected value or the standard deviation of a random variable, or do you feel those are not important? Do you not plan to cover the LLN and CLT, or do you restrict yourself to the versions for Bernoulli random variables? | |
| Sep 22, 2016 at 18:29 | history | closed |
Nate Eldredge Michael Greinecker Michael Renardy Douglas Zare Neil Strickland |
Not suitable for this site | |
| Sep 22, 2016 at 18:17 | comment | added | Michael Greinecker | I'm really clueless as to what the actual question is. | |
| Sep 22, 2016 at 18:15 | comment | added | Nate Eldredge | This might be a good question for matheducators.stackexchange.com, but it isn't about research level mathematics, so I don't think it can stay here. | |
| Sep 22, 2016 at 18:12 | comment | added | Boris Bukh | Making a natural sentence true and meaningful (and rigorous!) is not enough? What is your proposed alternative approach? | |
| Sep 22, 2016 at 18:01 | history | asked | Filippo Alberto Edoardo | CC BY-SA 3.0 |