The course requires a knowledge of measure theory. It covers the essential tools necessary for the study of statistics.
The following topics are covered :
Random variables, dependence and independence.
Expectations and conditional probability.
Convergence of sequences of random variables.
Martingales.
Aims
The course aims to give a basic knowledge of probability theory. It is an introduction to the main tools that are necessary to tackle the big problems of statistical analysis and stochastic processes. After this course, the student will be able to calculate conditional and non-conditional expectations and to study the convergence of sequences of random variables (including asymptotic law).