Probability

Teacher(s)

Bertrand Aurélie (compensates Segers Johan); Segers Johan;

Language

French

Main themes

The course covers traditional aspects of the probability theory but examines the concepts from the point of view of their use in statistical analysis. The probability model is described, as are the basic properties of probabilities. Then experiments are considered where the feature of interest can be modelled by a random variable (discreet, continuous, uni- and multivariate). The analysis of the random variable functions is presented and justified by its use in the analysis of statistic sampling distributions. The importance of the Central Limit Theorem is also highlighted.

Aims

At the end of this learning unit, the student is able to :
1	The course introduces students to the method of probabilistic reasoning and statistical analysis. These methods are useful in all fields of science which make use of random and/or experimental data (human, technical, medical and natural sciences). Particular emphasis will be laid on equipping students with the tools for studying Management Science and Economic and Management Science. By the end of the course, students should be able to understand and model the random aspects of certain simple experiments and calculate the probabilities of events of interest. They should also be able to apply these models to more complex real situations and to describe these phenomena by means of suitable random variables (uni - and multivariate). Students will also be shown how to study the properties of random variable functions and how these concepts lend themselves to application within the framework of the statistical analysis (sampling).

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.

Content

• Introduction to statistics
  
• The probability model: calculating probabilities, conditional probabilities, combinatorics
  
• Discrete random variables, including the binomial, geometric and Poisson distributions
  
• Continuous random variables, including the uniform, exponential and normal distributions
  
• Discrete and continuous random vectors: marginal, conditional and joint distributions; correlation
  
• Transformations of random variables: order statistics, sums
  
• Random sampling and the central limit theorem: empirical mean and variance, approximation of the binomial distribution by the normal one
  

Teaching methods

• Lectures: the teacher introduces the concepts through an application and then presents the abstract form
  
• Exercise sessions: the teacher gives students problems to solve and encourages them to look for the solutions themselves
  

Evaluation methods

• Written exam, closed book, with the help of a formula list and a pocket calculator. Exercises (multiple choice questions) and theory (open questions).
  
• An optional test covering exercises on the first part of the course material takes place during the course itself. Students performing well on the test can skip a number of questions at the exam.
  

Online resources

A list of formulas, additional exercises, solutions of exercises covered in the tutorials, and links to some useful websites are available on the MoodleUCL course page.

Teaching materials

• Wackerly, D., Mendenhall, W. and R. Scheaffer (2008), Mathematical Statistics with Applications, Duxbury Press, New York, 7th edition. (Chapitre 1 à 7)
• Syllabus "LINGE1113 - Probabilités" (J. Segers)

Faculty or entity

ESPO