Semester | Mand. | Option | Filières |
BA3 | x |
Lecture | 2 weekly |
Exercises | 2 weekly |
Study plan | Semester | Mand. | Option | Filières |
Mathématiques 2020-21 | BA3 | x |
Cursus | Sem. | Type |
---|---|---|
Mathematics | BA3 | Obl. |
1. Basic framework of probability theory
We will start by discussing the notion of a probability space and events on a probability space. We learn doing basic manipulations with events, and meet interesting notions like independence and conditional probabilities.
2. Random variables
Random variables can be seen as a generalization of events. We will discuss different types of random variables and several examples like uniform, binomial, Gaussian, Poisson random variables.
There are different ways of describing random variables - distribution function, density function, expectation, variance, moments, characteristic functions. We will look into those.
We will also meet random vectors, and revisit the concept of independence, correlation and conditional laws in the realm of random variables.
3. Limit theorems
Sometimes when one considers combinations of many random variables certain interesting patterns and structures, certain laws start to emerge. We will study some of such phenomena, including what are called laws of large numbers and the Central limit theorem. This requires first understanding the notion of limits in the realm of probability theory.
4. Varia
Time permitting, we will discuss some interesting probabilistic models like branching random walks, or some applications to other fields of mathematics.
Probability, independence, mathematical expectation, random variables, random vectors, limit theorems.
First year analysis and linear algebra of the Mathematics section.
Ex cathedra lecture and exercises in the classroom
Attend lecture regularly, solve the problems presented and write out the solutions, study the previous course material before the next course, go over the material before the exam.
Written exam
Introduction à la théorie des probabilités, R. Dalang et D. Conus.
A first course in probability, S.M. Ross.
Bachelor and Master-level courses in Probability and statistics
obligatoire
obligatoire
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
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