Probabilités

Bonjour!

Bienvenue sur l'espace de cours du cours de Probabilité.

Les informations & le matériel de cours seront disponibles sur Moodle. Les notes de cours seront mises à jour au fur et à mesure que le cours avance, quand une nouvelle version est disponible, elle sera postée en même temps que les exercices.

Les cours ont lieu les mercredi de 8h15 à 10h en CM 2 et seront donnés au tableau noir.

Les séances d'exercices ont lieu les mercredi de 10h15 à 12h en MA A1 10 et CE1105.

Tous deux commencent le 11.09.2024.

On utilisera ED Discussion (voir lien ci-dessous), n'hésitez pas à poser des questions!

Le système d'apparition des feuilles d'exercice sera:

• la série n sera disponible au plus tard la semaine n;
• les solutions de la semaine n seront discutés et disponibles la semaine n+1.
• la série 0 est discuté 11.09 à 10h ;)

Hopefully you are enjoying holidays, but the exercise sheet is attached below too.

Dear all,

There is no course this week, but to help you go through the material there is a Q&A session at 9h15 in CM 2 with my PhD student P. Bordereau. The material is given by the notes, starting from page 26.

The exercise class takes place as usual, but be aware that the assistant configuration is somewhat different.

For those who lack probability due to this, I've added a video about randomness in number theory too. ;)

We will meet on ZOOM this time:

https://epfl.zoom.us/j/66827564322?pwd=WEFoMnpVRFBkRS9EZkVNOU96bVJhUT09

Meeting ID: 668 2756 4322

Passcode: Fin22

Here is some material to help you with revision.

(You will soon find here a list of exercises to concentrate on for the exam, and a way to conceptualize the material, for now just last year's exam). 

We will meet on Wednesday 16/09 at 8.15 AM on ZOOM to discuss the content and the format.
The link is  here and the pass is PROB20

The first exercise class also takes place -- notice that it is before the course on Tuesday at 13h15. 
ZOOM link is here, pass is PROB20. There is also PIAZZA live Q & A. On campus please use room MA A3 31.

Sheet will be up here by Monday evening.

This week we learn to know the basic framework of modern probability.

I have prepared notes and videos, and as discussed - a group of you will fill in proofs, and we will discuss them next week.
The results that needs proofs are: Lem 1.3, Prop 1.4, Lem 1.6, Lem 1.7, Prop 1.8, Cor 1.11.
Some of them are direct, for those which are not I have given sketches. If there are issues, please write me and remember - we are still experimenting!
Please write these proofs on Piazza by Monday evening. You can also attach files to Piazza (.tex preferred, but can also be picture). 

I strongly encourage you to work together and go through each-others proofs before posting. This is the whole idea.
The google sheet for groups is now fixed, any further changes should be done between you, and by then contacting me saying that a switch has occurred.

Finally, please also notice that there is a Poll about a voluntary Latex course there. If interested, please sign up.

This comes in two parts - we discuss a bit further the probabilistic set-up, in particular the notion of measurable maps and probability measures on the real line; and the dig into very important probabilistic notions of conditional probability and independence.

I have prepared notes (we are not treating Bayes rule, part 1.2.3 just as yet) and videos, and as discussed - a group of you would fill in proofs, and we will discuss them next week.
The results that needs proofs are: Lem 1.13, Prop 1.14, Thm 1.16, Lem 1.18, Prop 1.19, Lem 1.21.

Please write these proofs on Piazza by Monday evening, say 18h. You can also attach files to Piazza (.tex preferred, but can also be picture). 

I strongly encourage you to work together and go through each-others proofs before posting. This is the whole idea.

We will meet on the course ZOOM tomorrow at 9h15 (the link is the usual one for the class) to first discuss the proofs, and roughly from 9h40 we discuss any questions you might have about this weeks session. 

This is our final week on the set-up of the framework, I promise that from next week the style will get lighter and separate from the met. & top. spaces course!

I have prepared notes  and videos, and as discussed - a group of you would fill in proofs, and we will discuss them next week.

The results that needs proofs are: Lem 1.28, Prop 1.29, Prop 1.31, Cor 1.36, Cor 1.37.
As always, if you don't manage to prove, just give your best effort!

Please write these proofs on Piazza by Monday evening, say 18h. You can also attach files to Piazza (.tex preferred, but can also be picture). 

I strongly encourage you to work together and go through each-others proofs before posting. This is the whole idea.

We will meet on the course ZOOM tomorrow at 9h15 (the link is the usual one for the class) to first discuss the proofs, and roughly from 9h40 we discuss any questions you might have about this weeks session. 

-----

On Monday, at 11:15am, we will have an introduction to Latex and Piazza. It should last at most until 12:15 but may end earlier depending on how fast we cover the material.

Here is the ZOOM link for the Latex & Piazza introduction. See you there!

We are now done with building the foundations for mathematical probability theory and will actually start taking care of the garden. In other words, this week we start with the central notion of probability - random variables. Things will get less heavy, but I hope, will remain interesting!

I have prepared notes and videos, and as discussed - a group of you would fill in proofs, and we will discuss them next week.
The results that needs proofs are: Lem 2.4, Lem 2.5, Lem 2.6, Prop 2.7, Lem 2.8, Lem 2.9. 

Please write these proofs on Piazza by Monday evening, say 18h. You can also attach files to Piazza (.tex preferred, but can also be picture). 

I strongly encourage you to work together and go through each-others proofs before posting!

We will meet on the course ZOOM tomorrow at 9h15 (the link is the usual one for the class) to first discuss the proofs, and roughly from 9h40 we discuss any questions you might have about this weeks session. 

Dear all,

Thanks for your feedback! 
This is a transition week, we still have several proofs to discuss, the videos are still meant to accompany notes. 

This week we will still meet on the course ZOOM tomorrow at 9h15 (the link is the usual one for the class) to discuss previous week's proofs and the future of proofs in general (i.e. who will prove the Riemann hypothesis?)

This week we will try a ZOOM class on Wednesday (tomorrow) at 8h15. Password is PROB20.

ZOOM videos are now up in the usual folder.

This week is a bit different: I have finished writing up proofs for Sections 1 and 2, and will put them up very soon.
In the light of this, there will be very little new material this week - maybe 1-2 short videos (we basically also just finished Section 2 too).

So your work main work this week should be going through the proofs of the material up to now.
In reworking notes, I tried to take into account your feedback (e.g. examples, clarifications), and also restructured a bit for clarity. 

All feedback, typos etc still very welcome!

PS! There is no ZOOM tomorrow, as I am not unfortunately available - but we will then do a longer session next week.

This weeks topic is mathematical expectation. I am running late with the materials (apologies!), but one thing is sure: we will meet on the course ZOOM tomorrow at 9h30 for a Q & A session. 

We will continue with mathematical expectation and introduce also the notion of variance and notion of moments.
Again the materials are waiting for the sunset, but we meet on the course ZOOM tomorrow at 9h40 for a Q & A session. 

PS! I believe you can again give feedback through the IS-academia, please do so independently whether you like or don't like the course - it is helpful to have your feedback in any case!
PS2! Another quiz for this course is also about to be ready!

We start a new chapter on limit theorems. This week we discuss infinite sequences of events and random variables, and see how surprisingly interesting things can be said by surprisingly elementary methods.

For those interested - we meet on ZOOM at 9h30 to first discuss the QUIZ and then the course.

I will try to put up material for both this and next week - the topics are almost sure convergence, strong laws of large numbers and the Central limit theorem.
If you prefer to cut it into two sessions, I recommend doing everything but the CLT this week, and CLT next week.

We meet tomorrow at 9h35 on ZOOM for Q & A. 

The last week -- Central Limit Theorem.
We can meet at 9h15 on ZOOM to discuss the exams, mock-exams, the revision, and also the content.