Duration
Part 1: Analysis tools for probabilities : 6h Th
Part 2: Probability theory : 20h Th
Number of credits
| Bachelor of Science (BSc) in Computer Science | 5 crédits |
Lecturer
Part 1: Analysis tools for probabilities : Laurent Loosveldt
Part 2: Probability theory : Laurent Loosveldt
Language(s) of instruction
French language
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Part 1: Analysis tools for probabilities
The aim of this course is to learn the basic notions of probabilities. In the first chapter, we present the formalism of events as well as a first approach of "everyday probabilites" based on combinatorics arguments. In order to develop a more formal approach, the second chapter deals with some tools from mathematical analysis. The axiomatic approach of proibabilities is the main point of chapter 3 where we focus on definining the notions of probability measure, conditional probability and independence of events. Random variables, which are the main objetcs of probabilities, are studied in chapter 4 while chapter 5 is devoted to the independence of random variables. In chapter 6, we give a first approach to the conditional expectation. Finally, in chapter 7, we present some "limit theorems" which will play a major role in statistical inference.
Learning outcomes of the learning unit
Part 1: Analysis tools for probabilities
The student will be able to recognize and solve elementary probabilistic problems.
Prerequisite knowledge and skills
Part 1: Analysis tools for probabilities
Elementary algebra, elementary calculus.
Planned learning activities and teaching methods
Part 1: Analysis tools for probabilities
Theoretical lectures and supervised problem solving sessions.
Mode of delivery (face to face, distance learning, hybrid learning)
Part 1: Analysis tools for probabilities
Face-to-face.
Part 1: Analysis tools for probabilities
The notes of the lectures are available on eCampus.
Slides and exercises lists will also be uploaded on ecampus.
List of the main reference:
- Michael Baron, Probability and Statistics for computer scientists, 3rd Edition, CRC Press, 2019.
- J.K Blitzstein et J. Hwang, Introduction to Probability, Taylor and Francis, 2019.
Part 1: Analysis tools for probabilities
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Other : Project
Additional information:
The final grade will be obtained after a written exam concerning both theory and exercises.
Work placement(s)
Part 1: Analysis tools for probabilities
None.
Organisational remarks and main changes to the course
Part 1: Analysis tools for probabilities
See eCampus
Contacts
Part 1: Analysis tools for probabilities
Laurent Loosveldt
Email : l.loosveldt@uliege.be
Département de Mathématique,
Allée de la Découverte, 12
4000 Liège Belgium
B37, Office 0/59