UCL - Probability

[INGE1113]

[30h + 15h] 4 credits

This course is taught in the 2d semester.

Teacher(s): Johan Segers

Language: French

Level: First

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

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).

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.

Content and teaching methods

Contents:
Introduction to statistics, the probabilistic model, discreet random variables, continuous random variables, multivariate variables, random variable functions, sampling and Central Limit Theorem, normal approximation to the binomial
The course comprises:
- lectures (the teacher introduces the concepts through a particular concrete application and abstracts from that),
- practical exercise sessions (the teacher gives students applications/problems and suggests ways of solving them). Active student participation through reading and independent problem solving

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Course materials : Wackerly, D., Mendenhal, W. and R. Scheaffer (2002), Mathematical Statistics with Applications, Duxbury Press, New York, 6th edition (chapitres 1 à 7)