Weekly outline

  • General

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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 room CM 1 120 on Wed 2-4 PM and in room INR 219 on Thu 8-10 AM

    Exercise sessions:
    - In person in room INR 219 on Thu 10-12 AM

    Grading scheme:
    - Graded homeworks 20%
    - Midterm 20%
    - Final exam 60%

    Principle for the graded homeworks: 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 5pm in the dropbox outside of INR 131.

    Midterm exam: Thursday, April 11 8:15am-10am, CM 1 3

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

    Final exam: Thursday 20.06.2024 from 09h15 to 12h15 (CE1).

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

    Course instructor:
    Prof. Yanina Shkel     || MIL - IPG || INR 131 || yanina.shkel@epfl.ch
    Teaching assistants:
    Marco Bondaschi || LINX - IPG || INR 136 || marco.bondaschi@epfl.ch
    Anuj Yadav || MIL - IPG || INR 034 || anuj.yadav@epfl.ch

    Course Webpage:

    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.

    Geoffrey R. Grimmett, David R. Stirzaker, One Thousand Exercises in Probability, 1st 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 (February 21-22)

    Wed: Sigma-fields (sections 1.1, 1.2, 1.3)
    Thu: Random variables (sections 1.4, 1.5), probability measures (section 2.1)

  • Week 2 (February 28-29)

    Wed: Probability measures, Distributions of random variables (sections 2.1, 2.2, 2.3, 2.4)
    Thu: The Cantor's set (Section 2.5);  Independence (sections 3.1, 3.2, 3.3, 3.4)

  • Week 3 (March 6-7)

    Guest Lecture by TAs Anuj and Marco this week!

    Wed: Independence (section 3.4); Do independent random variables really exist? (section 3.5); Convolution (section 3.6)
    Thu: No class! (Exercise session as usual)

  • Week 4 (March 13-14)

    Wed: Expectation (section 4), Characteristic function (section 5)
    Thu: Characteristic function (section 5), random vectors (section 6.1)

  • Week 5 (March 20-21)

    Wed: Gaussian random vectors (sections 6.2, 6.3)

    Thu: Inequalities (section 7); Convergences of sequences of random variable (sections 8.1, 8.2, 8.3)

  • Week 6 (March 27-28)

    Wed: Borel-Cantelli lemma;  Laws of large numbers - weak and strong, proof (sections 8.3, 8.4, 8.5)

    Thu:  convergence of the empirical distribution; (sections 8.6)

    NB: Because of the midterm next week, Hwk 6 is due on Thursday, April 17 only!

  • Week 7 (April 10-11)

    Wed: NO CLASS

    Thu, 8:15-10:00 AM, in room CM 13: Midterm
    - content: all the course + exercises until week 6 (except hwk 6)
    - allowed material: one cheat sheet (i.e., two single-sided A4 handwritten pages)

  • Week 8 (April 17-18)

    This week

    Wed: Kolmogorov’s 0-1 law, St-Petersburg paradox (sections 8.7, 8.8),  (section 9.1) 
    Thu: Convergence in distribution, equivalent definitions of convergence in distribution, Lindeberg's principle (sections 9.1, 9.3, 9.4)