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
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
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.
Part 1: Analysis tools for probabilities
The therory of probability relying on various basic notions of analysis, we devote a part of this course to them. We present:
- the series (useful to define the probability axioms)
- the double integrals (precious to consider couple of random variables)
- the exponential function and the Gauss integral (essential to define the Gaussian distribution)
Part 2: Probability theory
A first approach of the theory of probabilities will be presented, in the context of problems with finitely many equiprobable outcomes. Once the necessary tools from mathematical analysis acquired, we will tackle a more formal approach of the theory of probabilities. The course will then focus on
- the axioms of probability
- conditional probabilities (including Bayes formula and the law of total probability)
- random variables and their expectation/variance
- bivariate distributions and independence of random variables
- conditional expectation
- law of large number,s Central Limit Theorem and Borel-Cantelli Lemma
Learning outcomes of the learning unit
The student will be able to recognize and solve elementary probabilistic problems. He/she will also be able to apply probabilities in the contexts of elementary stochastic processes (course MATH1222-3) as well as statistical inference (course MATH0487-2).
Part 1: Analysis tools for probabilities
The student will be able to manipulate the tools from analysis listed here over in the context of basic probabilistic problems.
Part 2: Probability theory
The student is expect to master the notions of probability learned during the lectures and listed above. In particular, he/she will be able
- to present the theoretical aspect concerning these notions
- recognise and resolve basic problems in probability
Prerequisite knowledge and skills
Elementary algebra, elementary calculus.
Planned learning activities and teaching methods
Theoretical lectures and supervised problem solving sessions.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Further information:
Face-to-face.
Recommended or required readings
Platform(s) used for course materials:
- eCampus
- MyULiège
Further information:
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.
Assessment methods and criteria
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Further information:
The written exam will be divided in two parts:
- one part devoted to the theoretical aspects, where the student is expected to define notions and prove results which were presented during the lectures.
- one part devoted to the exercices, where the student is expect to solve problems in probability which are similar to the ones met during the exercises sessions
Work placement(s)
Organisational remarks and main changes to the course
Contacts
Laurent Loosveldt
Institut de Mathématique - B37 - Bureau 0/59
Quartier Polytech 1
Allée de la découverte, 12
4000 Liège (Sart-Tilman)
Tél. : (04) 366.92.56.
E-mail : l.loosveldt@uliege.be