Aperçu des semaines

  • Généralités

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    "Probability theory is nothing but common sense reduced to calculation." Pierre-Simon de Laplace, 1812 (see other interesting quotes from Pierre-Simon de Laplace)

    Lectures:

    • In-person in the room INR 219 on Wed 1-4 PM and INM 10 on Thu 9-10 AM.

    Exercise Sessions:

    • In-person in the room INM 10 on Thu 10-12 AM.

    Grading Scheme:

    • Graded homework - 20%
    • Midterm - 20% 
    • Final exam - 60%

    Principle for the graded homework: each week, one exercise is starred and worth 2% of the final grade; the best 10 homeworks (out of 12) are considered. The homework is due on Wednesday of the following week, in lecture or by 5 pm in the dropbox outside INR 131.

    Midterm Exam: Thursday, October 31 (Tentative).

    •  Allowed material: one cheat sheet (i.e., two single-sided A4 handwritten pages).

    Final Exam: TBD.

    • Allowed material: two cheat sheets (i.e., four single-sided A4 handwritten pages).
    • Please note that the exam content will focus more on the second part of the course (but also on the first part).

    Course Instructor:

    Prof. Yanina Shkel     || INR 131 || yanina.shkel@epfl.ch
    Teaching Assistants:

    Cemre Çadir || INR 031 || cemre.cadir@epfl.ch
    Anuj Yadav || INR 034 || anuj.yadav@epfl.ch

    Course Webpage:


    References:

    • Sheldon M. Ross, Erol A. Pekoz, A Second Course in Probability, 1st edition, 2007.
    • Jeffrey S. Rosenthal, A First Look at Rigorous Probability Theory, 2nd edition, World Scientific, 2006.
    • Geoffrey R. Grimmett, David R. Stirzaker, Probability and Random Processes, 3rd edition, Oxford University Press, 2001.
    • Sheldon M. Ross, Stochastic Processes, 2nd edition, Wiley, 1996.
    • William Feller, An Introduction to Probability Theory and Its Applications, Vol. 1&2, Wiley, 1950.
    • (more advanced) Richard Durrett, Probability: Theory and Examples, 4th edition, Cambridge University Press, 2010.
    • (more advanced) Patrick Billingsley, Probability and Measure, 3rd edition, Wiley, 1995.


    Mediaspace channel for the course (please note that these videos were made for a previous version of the course taught by Olivier Lévêque: there will be some differences with this year's version)

    Recordings of live lectures (from 2023, Olivier Lévêque)

  • Week 1 (September 11-12)

    Wed: Sigma-fields and random variables (chapter 1); probability measures (section 2.1)
    Thu: Probability measures (section 2.1)

  • Week 2 (September 18-19)

    Wed: Probability measures and distributions (sections 2.2-2.5); independence (sections 3.1, 3.2)
    Thu: Independence (sections 3.1, 3.2)

  • Week 3 (September 25-26)

    Wed: Independence (section 3.2-3.6); expectation (chapter 4)

    Thu: Expectation (chapter 4)