University of Liege | Version française
	Study programmes 2010-2011 Last update : 11/04/2011
	MATH0482-1   Probability and Statistics II Duration :   25h Th, 10h Pr Credits/ECTS :   Bachelor in mathematical sciences, 2nd year Second semester 3 One-year preliminary programme leading to the Master in Statistics, general orientation Second semester 3 Holder(s) :   Paul Gérard Language :   French language Course contents :   The course is a continuation of the course "probability and statistics" of the first year of the bachelor in mathematics program. It first gives a summary (avoiding most of the demonstrations) of the main notions and results of the theory of measure and integration needed for a mathematical approach of the probability theory. After this summary, the content of the course is as follow: Random variables and their distributions (join, marginal, conditional) Usual probability laws Independence Expectation and moments of a random variable, conditional expectation and variance Correlation and regression Convergence almost sure, in probability, in law, in P-L2 Characteristic function and moments generating function Laws of the great numbers and central limit theorems. Course objective :   To master mathematically the main notions and facts about random variables and probability measures. To open several ways towards applications. Prerequisites :   The course "probabilité et statistique" from the program of the first year of the bachelor degree in mathematics or an mathematical introductory course to the concept of probability. Workshops :   Exercices about classical distributions and some applications directed to statistics. Organization :   The course will be illustrated through exercices and examples. Short personnal works may be given. Written notes :   References: Initiation aux probabilités. Sheldon.M.Ross. Presses polytechniques romandes. Cours de probabilités. Alain Monfort. Economica. Collection « économie et statistiques avancées ». Assessment :   Exercices: written examination Théory: oral examination Contacts :   Paul GERARD, Institut de mathématique, B37 Grande Traverse 12, Sart-Tilman 4000 Liège Tél.: 00-32-(0)43.66.93.84 Fax: 00-32-(0)43.66.95.47 Couriel: paul.gerard@ulg.ac.be Home Search by Faculty Search by teacher Search by course code and title
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