Teacher(s)
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). 
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 (on paper or on a computer). Exercises (multiple choice and/or numerical and/or open questions).

An optional test (with exercises in multiple choice and/or numerical and/or open questions) covering exercises on the first part of the course material takes place during the course itself (if the sanitary situation allows it). 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