Probability and statistics 2 - 3MMPS2

Informations générales

  • Number of hours

    • Lectures 24.0
    • Projects -
    • Tutorials 24.0
    • Internship -
    • Laboratory works -
    • Written tests -

    ECTS

    ECTS 4.0

Goal(s)

This course offers a deepening and extension of the concepts of probability calculus and statistical inference introduced in the course Probability and Statistics 1. The course follows an approach based on mathematical formalization.
The course is recommended for students interested in applied mathematics, financial engineering, and the foundations of data science and artificial intelligence.

Responsible(s)

Olivier GAUDOIN, Pierre ETORE

Content(s)

  • Axioms and basic definitions in probability, link with integration.
  • Random variables and vectors, probability distributions.
  • Conditioning, conditional expectation.
  • Convergence of sequences of random variables, asymptotic theorems (strong law of large numbers, central limit theorem, etc.).
  • Statistical estimation: estimation methods, quality and optimality of an estimator, quantity of information.
  • Asymptotic results in statistics.
  • In-depth study of hypothesis testing.

Prerequisites

Prerequisites are a basic knowledge of mathematics and probability, and the equivalent of the course Probability and Statistics 1.

The course uses notions of elementary measure theory and Lebesgue integrals from the Analysis and Calculus for Engineers course.

Test

Evaluation : 25% of Examen écrit and 75% of Examen écrit (3h)

Resit : Examen écrit (3h)

Session 1:

  • Continuous assessment: written exam (1h30). Handwritten documents allowed. Weight: 25%.
  • Final exam: written exam (3h). Handwritten documents allowed. Weight: 75%.

Session 2: written exam (3h). Handwritten documents allowed. Weight: 100%.

Calendar

The course exists in the following branches:

  • Curriculum - Core curriculum - Semester 6
see the course schedule for 2026-2027

Additional Information

Course ID : 3MMPS2
Course language(s): FR

You can find this course among all other courses.

Bibliography

Ph. BARBE et M. LEDOUX : Probabilité, EDP Sciences, 2007.
B. CADRE et C. VIAL : Statistique mathématique, cours et exercices corrigés, Ellipses, 2012.
G. SAPORTA : Probabilités, analyse de données et statistique, Technip, 2011.
V. PANARETOS : Statistique pour mathématiciens: un premier cours rigoureux, EPFL Press, 2024}