2023-2024 / STAT0067-4

Probability and statistical inference


35h Th, 30h Pr

Number of credits

 Bachelor in economics and business management6 crédits 


Célia Paquay

Language(s) of instruction

French language

Organisation and examination

All year long, with partial in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

1st part : Probability Theory

- Bases: Random situations, events and probability, conditioning, probability trees and independance
- Random variables and probability distribution
- Typical probability distributions (discrete and continuous)
- Multivariate r.v.
- Functions of r.v.

2nd part : Statistical inference

- Principles of inferential statistic: object, variables, observations, population and sample, sampling and sampling distribution
- Point estimation (estimators : properties and construction)
- Confidence interval estimation
- Statistical tests (principle and power, conformity, independence, several samples and populations)

Learning outcomes of the learning unit

This course aims to:

  • enable the student to understand the calculation of probabilities and to model random phenomena
  • provide the necessary probabilistic bases for inferential statistics
  • master the basic principles and methods of inferential statistics (estimating and testing hypotheses) and to know how to apply these in concrete contexts and to interpret the results.
Broadly speaking, the course will achieve the following overall objectives:

  • The course will allow the student to show critical thinking and scientific rigor in the analysis of a complex situation.
  • The course will encourage the student to be autonomous and an entrepreneur in his learning.
A more precise list of specific objectives to be achieved is presented in the course syllabus.

Prerequisite knowledge and skills

  • Basic algebra: order of operations, fractions, distributive property, use of parentheses, remarkable products, use of summation symbol
  • Function of variables: knowing how to graph linear functions, use of the correct vocabulary (abscissa, ordinate, sloped,...)
  • Properties of the exponential and logarithmic functions
  • Descriptive statistics: among others, definitions and properties of mean, variance, Chebychev's theorem; for bivariate series, definitions and properties of covariance, linear correlation; the principle of variance decomposition
  • Elements of differential and integral calculus: knowing how to integrate polynomials, knowing how to perform partial derivatives (finding the maximum of a function with several variables)

Planned learning activities and teaching methods

The sessions are mainly based on the presentation of the theoretical frame by the teacher and the practice of exercices and applications by the students. The teacher expects the students to actively participate during the sessions, for instance via Wooclap or other surveys.
Some sessions will be dedicated to practical exercises.
The teacher uses Excel and Geogebra to provide illustrations of several concepts of the course. Students are invited to learn to use those softwares, but  this learning is not assessed.

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

Face-to-face course

Additional information:

Ex-cathedra sessions where the presentation of theoretical concepts and the resolution of exercises by the students will be mixed. Some sessions will be particularly dedicated to exercises in order to allow students to face the subject and ask their questions to the teacher.

Recommended or required readings

Course notes, syllabus with additional exercises and slides per chapter available on Lola.

References used to write down the notes
[1] Catherine Dehon, Jean-Jacques Droesbeke, and Catherine Vermandele. Eléments
de statistique : 6e édition revue et augmentée. Editions de l'Université de
Bruxelles/Editions Ellipses, 2015.
[2] Gentiane Haesbroeck. Probabilité et statistique I, 2007. Course notes at Sciences
Faculty, University of Liege.
[3] Bernard Lejeune. Probabilités et inférence statistique, 2005. Course notes at HEC-
[4] Brigitte Tribout. Statistique pour économistes et gestionnaires. Pearson Education
France, 2013.
[5]Newbold, P., Carlson, W. L., & Thorne, B. M. (2013). Statistics for business and economics (Global ed. ed.). Harlow: Pearson.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Additional information:

Partial examen in January on the part "Probability" and in June on the part "Inferential Statistics".

1st and 2nd session : individual written closed book exam with open questions for the two parts "Probability" and "Inferential Statistics". A scientific (non graphical) calculator is alload. The form and distribution tables will be provided during the exam.

If both grades are (strictly) greater than 7/20, the global grade will be the weighted average of the partial grades (40% for probability and 60% for inferential statistics). Otherwise, it will be the smallest of the values.

In case of a resit, an exemption will be automatically given for the possible passed part (at least 10/20). In case of a resit failure, no partial exemption will be given for next year.

Work placement(s)

Organisational remarks and main changes to the course

Lessons will not be recorded.



Célia Paquay
HEC- Management School of the University of Liege (building N1)
e-mail : cpaquay@uliege.be
Office: N1 - 308

Teaching Assistant

Emeline Leloup
HEC- Management School of the University of Liege (building N1)
email: emeline.leloup@uliege.be
Office: N1 - 310

Association of one or more MOOCs