Probability and statistics

This module introduces the fundamental concepts of probability calculus and the basic tools of one- and two-dimensional descriptive statistics.

Key words :

• Probability calculus: discrete random variable, continuous random variable, multidimensional random variable, usual probability laws, asymptotic theorems.
• Descriptive statistics, graphs, numerical indicators, links between two variables.

Prerequisites for this module include the integration of a function of one real variable, notions of series and optimization, as well as basic matrix calculus and linear algebra.

Part 1: Probability (5 sessions of 1h20 CM; 8 sessions of 1h20 TD)

Chapter 1: Axiomatic foundations of probability

Chapter 2: Random variables

Chapter 3: Usual laws of probability

Chapter 4: Pair of random variables

Chapter 5: Random vectors

Chapter 6: Convergence and "asymptotic" theorems

The "Probabilities" section is the subject of a written test during the semester, lasting 1h30, with authorized documents (coef. 2).

IMPORTANT: The teaching of this "Probability" section begins in Chapter 4. The concepts and skills associated with the first three chapters are considered acquired. Students needing a refresher on these first 3 chapters can take the differentiated "Mathematics" course at the very beginning of Semester 5. The same applies to students needing a refresher on basic linear algebra and matrix calculus, notions that are highly useful in the context of random vectors presented in Chapter 5.

Part 2: Descriptive statistics (4 sessions of 1h20 of CM; 4 sessions of 1h20 of TD)

Chapter 1: General introduction

Chapter 2: Presentation of statistical series

Chapter 3: Graphical representations

Chapter 4: Numerical summaries of one-dimensional statistical series

Chapter 5: Studying two-dimensional statistical series

The "Descriptive Statistics" section is the subject of a written test at the end of the semester lasting 1 hour, with documents allowed (coef. 1).

 Authorized documents (da) for parts 1 and 2 tests:

Only one double-sided A4 sheet of personal, handwritten notes is allowed for examination papers (in sessions 1 and 2). Photocopies are not permitted. This document will be returned with the exam paper, and will be returned at the student's request after marking.

"TD Philosophy:

• Part 1 (Probability): TDs consist in solving exercises or problems in probability calculus or applied probability to illustrate the concepts covered in the course. Some of the exercises are more theoretical, but most involve modeling real-life problems.
• Part 2 (Descriptive statistics): TDs consist in solving exercises or problems in one- or two-dimensional descriptive statistics to illustrate the concepts presented in class. Most of the exercises involve the processing of real data from a variety of problems. 

Remarks:

• There are no practical exercises associated with this course. Practical implementation of the "Descriptive statistics" section using R statistical software will be carried out in semester 6 as part of module CO6SFMA1 "Inferential statistics and data analysis".
• There is no project associated with this course. Practical implementation of the "Descriptive statistics" section using R statistical software will be carried out in semester 6 as part of module CO6SFMA1 "Inferential statistics and data analysis".

Applied mathematics