Aims

Probability theory is a branch of mathematics allowing for describing and understanding
random experiments. It is the key tool to measure and control the uncertainty inherent
to the statistical reasoning. This course aims to develop the probabilistic theory for
(countably or uncountably) infinite sample spaces, extending the methods presented in
the former course devoted to descriptive statistics. Multivariate probabilistic models are also
considered.
Emphasis is put on applications, with statistical procedures in mind. Simple examples
demonstrate the usefulness of probability theory in sampling techniques and statistical
inference.

Main themes

Part I:
Random variables (distribution function, mathematical expectation, uniform distribution,
exponential distribution, normal distribution, binomial distribution, Poisson distribution)
Part II:
Random vectors (covariance matrix, linear combination, multivariate normal)
Part III:
Sampling theory (population, sample, sample average distribution, sample proportion
distribution, law of large number, central limit theorem)

Content and teaching methods

Contenu et méthodes
The course is organised as follows:
- ex caethedra lessons
- practical sessions during which students are invited to solve exercises with the help
of teaching assistants
- individual problem solving and complementary readings

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Course materials : Wackerly, D., Mendenhal, W. and R. Scheaffer (2002), Mathematical Statistics with Applications, Duxbury Press, New York, 6th edition (chapitres 1 à 7)

Other credits in programs