2020-2021 / MATH0062-1

Elements of probability calculus

Duration

15h Th, 10h Pr, 25h Proj.

Number of credits

 Bachelor of Science (BSc) in Engineering3 crédits 

Lecturer

Pierre Sacré

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

  • Motivations: reasoning under uncertainties, modeling of stochastic systems, data analysis.
  • Basics: random experiment, events, Kolmogorov axioms, conditional probability, Bayes theorem, independence, interpretations of the notion of probability.
  • Discrete and continuous random variables: probability distribution, repartition function, density, expectation, variance, moments, characteristic and generating functions, usual distributions, functions of a random variable.
  • Pairs and vectors of random variables: joint, marginal, and conditional distributions, conditional expectation and variance, independence, covariance/correlation, functions of random variables, linear and nonlinear regression.
  • Convergence of sequences of random variables, central limit theorem, laws of large numbers.
  • Notion of random function.

Learning outcomes of the learning unit

The student shall be able to apply probabilistic methods to problems of reasoning under uncertainty, by being able to model them and identify the main resolution steps. He will also be knowledgeable about the main analytical and computational techniques useful to compute numerical solutions.

Prerequisite knowledge and skills

Calculus, algebra, geometry, and elements of computer science and applied mathematics.

Planned learning activities and teaching methods

The course is composed of about 12 hours of theoretical lectures, 10 hours of classroom exercises, and 25 hours of assistance to the realization of practical projects with the computer.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face or distance-learning depending on the evolution of the sanitary situation.
 

Organisational adjustments related to the current health context

Recommended or required readings

The course notes, slides, and exercise notes will be available on the course's webpage at the beginning of the semester: http://www.montefiore.ulg.ac.be/~sacre/MATH0062/.

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

Any session :

- In-person

written exam ( open-ended questions )

- Remote

written exam ( open-ended questions )

- If evaluation in "hybrid"

preferred in-person


Additional information:

The assessment is composed of two grades: a grade for the personal projects (approximately 20% of the final grade) and a grade for the written exam covering theory and exercises (approximately 80% of the final grade).
The projects and the written exam are mandatory. An absence for one of these parts will result in an absence for the course.

Work placement(s)

Organizational remarks

Contacts

Lecturer: Pierre Sacré (p.sacre@uliege.be).
Webpage: http://www.montefiore.ulg.ac.be/~sacre/MATH0062/.