Weekly outline

  • General

    DISCLAIMER: The program below is that of the 2018-2019 edition of the course. The present page will be updated in January 2020.

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

    The course starts on Wednesday, February 20, 2019, at 1:15 PM in room *INM 10*

    Course schedule:

    - Lectures on Wednesday // 1:15-4:00 PM // room INM 10

    - Exercise sessions on Thursday // 9:15-11:00 AM // room INR 113

    - Additional recitation sessions (starting March 18) on Monday // 11:15 AM - 12:00 PM // room INR 113 (except on April 1st, in room INF 119)

    Grading scheme: 5 graded homeworks (4% each) + 2 bonus exercises (1% each)
                                     + midterm 20%; total capped at 40%
                                     exam 60%

    Course instructor: Olivier Lévêque // LTHI // INR 132 // 021 693 81 12 // olivier.leveque@epfl.ch

    Teaching assistants: Amedeo Esposito // LINX // INR 031 // 021 693 12 29 // amedeo.esposito@epfl.ch
                                            Pierre Quinton // LTHI // INR 030 // 021 693 75 14 // pierre.quinton@epfl.ch
    References
    :

    Sheldon M. Ross, Erol A. Pekoz,  A Second Course in Probability, 1st edition, www.ProbabilityBookstore.com, 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.

    (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.

    Exams:

    Midterm exam on Thursday, April 11, 8:30 - 11:00 AM, in room CM 1 121
    Content of the exam: everything from week 1 until week 7
    Allowed material: two handwritten single-sided A4 pages

    Final exam on Thursday, July 4, 12:15 - 3:15 PM, in room CO 2
    Content of the exam: everything from week 1 until week 14
    Allowed material: four handwritten single-sided A4 pages

  • Week 1 (February 20-21)

    Sigma-fields, random variables (section 1)

  • Week 3 (March 6-7)

    Independence (section 3)
    Convolution (addendum)

    [From now on, changes with respect to the order of the existing lecture notes will be indicated in boldface. Additional lecture notes will be provided for the material that is not part of the original lecture notes].

  • Week 4 (March 13-14)

    Expectation (addendum and sections 4.1, 4.2)
    Characteristic function
    (addendum and section A.1)

  • Week 5 (March 20-21)

    Gaussian random vectors (addendum)

  • Week 6 (March 27-28)

    Inequalities (section 4.3)
    Convergences of sequences of random variables (sections 5.1, 5.2 and 5.3)

    Reminder: recitation session on Monday, April 1, in room INF 119

  • Week 7 (April 3-4)

    Borel-Cantelli lemma, laws of large numbers - weak and strong (sections 5.4 and 5.5)
    Convergence of the empirical distribution, Kolmogorov's 0-1 law (sections 5.6 and 5.7)

    Q&A session on Monday, April 8, at 11:15 AM, in room INR 113

  • Week 8 (April 10-11)

    St Petersburg's paradox and extension of the weak law (section 5.8)
    Convergence in distribution (section 6.1)
    Curie-Weiss model
    (addendum)

    Midterm exam on Thursday, April 11, 8:30 - 11:00 AM, in room CM 1 121
    Content of the exam: everything from week 1 until week 7
    Allowed material: two handwritten single-sided A4 pages

    • Week 9 (April 17 & 29)

      Lindeberg's principle, central limit theorem (sections 6.2 and 6.3)
      Alternate derivation of the central limit theorem (section A.2)

      Exercise session on Thursday, April 18, is cancelled and replaced by a recitation session on:
      Monday, April 29, 10:15 AM - 12:00 PM, in room INR 113.

    • Week 10 (May 1-2)

      Distances for convergence in probability and convergence in distribution (addendum)
      Coupon collector problem (addendum)
      Moments and Carleman's theorem (section A.4)

      Recitation session exceptionally on Monday, May 6, at 10:15 AM (and until 11:00 AM)

    • Week 11 (May 8-9)

      Hoeffding's inequality (section 7.1)
      Large deviations principle (section 7.2)
      Conditional expectation (part II, section 1 and addendum)
    • Week 12 (May 15-16)

      Conditional expectation (cont'd)
      Martingales: definition and basic properties (part II, section 2.1)
      Stopping times and optional stopping theorem (part II, sections 2.2 and 2.3)
    • Week 14 (May 29)

      NB: Course starts at 2:15 PM on that day

      Azuma's and McDiarmid's concentration inequalities (part II, section 3.7)
      Central limit theorem revisited: Stein's method (addendum)

      No exercise session on Thursday, May 30 (Ascension)

    • Revision week (June 25)

      Q&A session on Tuesday, June 25, 10:00 AM - 12:00PM, in room INR 113

      • Exam week (July 4)

        Final exam on Thursday, July 4, 12:15-3:15 PM, in room CO 2

        Allowed material: four handwritten single-sided A4 pages