Probabilities and statistics (I) [ LBIR1203 ]

LBIR1110  Math I

LMAT1111E  Math II

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 one-mean-confidence intervals.

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;

Regular courses and supervised practical exercises

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

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