Probability and Mathematical Statistics 1

1) The course provides basic notions and methods of probability theory, based on measure theory. Fundamentals will be taught to students at the level required for their further study in mathematics.
2) The course aims at giving precise and systematic knowledge on real and vector random variables (laws, moments, independence, conditional laws etc.). This is required for an appropriate understanding of probabilistic models and for further study in statistics, stochastic processes and stochastic calculus.
3) Within the course the most important limit theorems of the theory of probability will be carefully presented (laws of large numbers and central limit theorem). Basic applications will be given, in particular to statistics.
4) In the laboratory, fundamental notions will be given on generation of random numbers with preassigned distributions and the most basic applications of these techniques will be presented.

Students will acquire the basics of probability theory required to further pursue their study towards mathematics or its applications, either in mathematical statistics or in stochastic processes or in stochastic calculus and its applications.