Probability and statistics [INFCB213]

Learning outcomes

At the end of the course, the student should be able to • to carry out a descriptive statistic and • to pose a hypothesis test and solve it, in order to interpret the reality hidden by the data set, • to use the R language wisely to manipulate its data, • use the foundations of combinatorial analysis and probability calculus to determine the probabilities associated with different events, • use the foundations of functional analysis, linear algebra and discrete mathematics to determine the probability laws of random phenomena, • manipulate the usual theoretical laws to explain behaviour, • manipulate the laws associated with random variables studied simultaneously.

Content

The aim here is to provide the student with a deep and accurate understanding of the fundamental concepts as well as training in probabilistic and statistical reasoning. The mathematical formalism is simplified but present. The aim is to use the theory of measurement in an intuitive way to extend the concept of enumeration towards an analytical definition of probability laws. The basic subject of probability calculation is introduced by a few hours of descriptive statistics (treatment of a table of numbers, calculation of average, variance,...) which give rise to practical exercises with R. The principles of probability necessary for an introduction to inferential statistics are also defined. The course will focus on the basic techniques of parameter estimation and hypothesis testing.