This course is conceived to introduce the student to the fundamental concepts of probability theory. The course aims at getting a certain intuition of these concepts by the study, technically simple, of discrete and continuous probabilized spaces.
At the end of the course, students will have developed a global understanding of probability theory. Students will be able to define and use random variables (binomial, Poisson, normal, r.v. defined via a density). They will also be able to discuss convergence of sequences of random variables.
Introduction to the concepts of combinatory calculus, random variables, probability spaces. The properties of discrete random variables are studied such as the excepted value, variance, covariance, etc, of a random variable.
Chapter I :Chapter II: Conditional probability and independence.
Chapter III: Discrete and continuous random variables.
Chapter IV: Bivariate random vectors.
Chapter V: Stochastic convergences.
Exercices about all the concepts explained during the lecture.
The examination is in an oral and writing form. The written examination consists in several exercise items. During the oral examination, each student draws randomly a question about the theory and presents it. A second question is proposed by the professor. The preparation lasts roughly an hour. The presentation of the answers lasts approximately 15 to 20 minutes per student.
In case the situation requires distance evaluations, there will still be two exams. The written exam will be open book, with open exercice questions. Evaluating the theory will proceed in the same way.
Notes will be provided on Webcampus. They include the slides and associated recordings, as well as a syllabus (made available during the semester).
Reference book: Sheldon Ross, A first courses in probability, Prentice Hall, NY
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelier en sciences mathématiques | Standard | 0 | 4 | |
| Bachelier en sciences mathématiques | Standard | 1 | 4 |