| Course label : | Probability 1 |
|---|---|
| Teaching departement : | EEA / Electrotechnics - Electronics - Control Systems |
| Teaching manager : | Mister PIERRE-ANTOINE THOUVENIN / Mister PIERRE CHAINAIS |
| Education language : | |
| Potential ects : | 0 |
| Results grid : | |
| Code and label (hp) : | MR_DS_S1_PR1 - Probability 1 |
Education team
Teachers : Mister PIERRE-ANTOINE THOUVENIN / Mister PIERRE CHAINAIS
External contributors (business, research, secondary education): various temporary teachers
Summary
Fundamentals of probability and integration. First applications. - Probability space: the triplet (set, sigma-algebra, measure), examples (2h) - Random variables, random vectors, random element, examples (2h) - Expectation, variance, covariance, independence (2h) - Gaussian vectors: definition, density, rotational invariance (4h) - Projection’s theorem, L^2 space, conditional expectation, examples (Gaussian, ...) (4h) - Modes of convergence: in distribution, in probability, almost surely, L^p, examples (LLN) (2h) - Classical probability distributions and models (4h) - Characteristic function, the central limit theorem, examples (4h)
Educational goals
After successfully taking this course, a student should: • understand the mathematical structures of probabilistic modeling • be able to compute the main features of probabilistic models: location and scale parameters
Sustainable development goals
Knowledge control procedures
Continuous Assessment
Comments: Exam, credits, grading scale: (min) 0 – 20 (max) - Passing grade = 10/20
Online resources
1. https://www.statlect.com/fundamentals-of-probability/ 2. “Probability and Measure”, P. Billingsley 3. “Aléatoire”, S. Méléard
Pedagogy
24 hours, 8 lectures 4 exercises sessions Language of instruction is specified in the course offering information in the course and programme directory. English is the default language.
Sequencing / learning methods
| Number of hours - Lectures : | 12 |
|---|---|
| Number of hours - Tutorial : | 12 |
| Number of hours - Practical work : | 0 |
| Number of hours - Seminar : | 0 |
| Number of hours - Half-group seminar : | 0 |
| Number of student hours in TEA (Autonomous learning) : | 0 |
| Number of student hours in TNE (Non-supervised activities) : | 0 |
| Number of hours in CB (Fixed exams) : | 0 |
| Number of student hours in PER (Personal work) : | 0 |
| Number of hours - Projects : | 0 |
Prerequisites
Fundamental notions of mathematics.