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Probability theory

Code: C1222, ECTS: 2

Syllabus

This course describes the basic notions and methods of probability within a modern formal context. This discipline is playing an increasingly important part in the various engineering sciences, in modelling or through simulations; it is also a prerequisite for a sound understanding of methods commonly used in statistics.

Programme

  • Random experiment, probability of an event; independence of events; conditional probability;
  • Random variables, laws and densities, real and vectorial cases; independent variables;
  • Moments of random variables, mathematical expectation, covariance matrix;
  • Conditioning: conditional laws in a couple (X, Y), expected variable and regressions;
  • Transformation of a random variable, real and vectorial cases, convergence in law;
  • Gaussian variables and vectors; central limit theorem, covariance matrix;
  • Point processes: point definition, random counting function; study of the Poisson process;
  • Indications on convergences of random variables, laws of large numbers.

Teaching team

Lecturer(s)
Silvère BONNABELMichel SCHMITT

Teaching staff
Mazyar MIRAHIMIJulien REYGNERCARRIZO VERGARA RICARDO
Alain SARLETTE

Code C1222
Year 1st year
Level Undergraduate
ECTS Credits 2
Coefficient 2
Nb. of hours 25
Nb. of lessons 20
Course type Fundamentals
Semester 2
Period Spring
Domains
  • Mathématiques
  • Probabilités et statistiques
Last update:
03 Feb 2017 10:16 by valerie