Teacher(s)
Bogaert Patrick;
Prerequisites
LBIR1110 Math I
LMAT1111E Math II
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE)
for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
Introduction to the calculus of probability  Discrete and continuous random variables: probability and probability density functions, expectations, variance and other statistical properties  Principal statistical distributions  Couples of random variables and random vectors: joint, marginal and conditional distributions, independence, covariance and correlation, expectations and conditional variance  Introduction to statistics  Notions concerning estimators and estimator properties  Inference about the mean and variance: estimators, sample distributions  Notions of onemeanconfidence intervals.
Aims
At the end of this learning unit, the student is able to : 
1 
a. Contribution of this activity to the learning outcomes referential :
1.1, 2.1
b. Specific formulation of the learning outcomes for this activity
A the end of this activity, the student is able to :
· Name, describe and explain the theoretical concepts underlying the probability theory;
· Use the mathematical expressions in a formal way and by using rigorous notations in order to deduce new expressions or requested theoretical results;
· Translate mathematically textual statements using a rigorous mathematical and probabilistic framework by relying on appropriate concepts and theoretical tools;
· Solve an applied problem by using a deductive approach that relies on a correct use of well identified properties and expressions;
· Validate the internal consistency of the mathematical expressions and results based on theoretical properties and logical constraints that are induced by the probabilistic framework;


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 the calculus of probability  Discrete and continuous random variables: probability and probability density functions, expectations, variance and other statistical properties  Principal statistical distributions  Couples of random variables and random vectors: joint, marginal and conditional distributions, independence, covariance and correlation, expectations and conditional variance  Introduction to statistics  Notions concerning estimators and estimator properties  Inference about the mean and variance: estimators, sample distributions. Notion of confidence intervals.
Teaching methods
Regular courses and supervised practical exercises
Evaluation methods
Evaluation: Open book written examination (only with the original material). The examination is composed of exercises to be solved. Its duration is about 3 hours.
Other information
The course relies on a book which is considered as mandatory and must be bought :
P. Bogaert (2005). Probabilités pour scientifiques et ingénieurs. Editions De Boeck