This course aims to present a formal theory of probability based on Lebesgue's theory of measure and integration.
This course is designed to familiarise the student with the fundamental concepts of probability theory. The first part of the course aims to create some intuition of these notions through the study of discrete probability spaces. The second part is an introduction to probability measures on the real line. The main concepts studied are: discrete random variables, fundamental notions of probability calculus, independence, sequence of independent random variables, characteristic functions, central limit theorem, conditional expectation.
The evaluation of the course consists of two parts. 1) An individual oral exam which aims to evaluate the student's knowledge and level of understanding of the course (definitions, statements and proofs of theorems, synthesis questions...). 2) A written examination of exercises which aims to test the student's ability to apply the results seen in the course. If the student has a mark higher than 10/20 in the written and oral exams, the final mark is the arithmetic average of the two marks. Otherwise the final grade is the integer part of the geometric mean of the two grades.
Powerpoint slides projected during the course, and available on the course's webcampus2017 site.