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Sylvie Méléard,
Jean-René Chazottes,
and
Carl Graham
Ce cours d'introduction aux probabilités a la même contenu que le cours de tronc commun de première année de l'École polytechnique donné par Sylvie Méléard.
Le cours introduit graduellement la notion de variable aléatoire et culmine avec la loi des grands nombres et le théorème de la limite centrale.
Les notions mathématiques nécessaires sont introduites au fil du cours et de nombreux exercices corrigés sont proposés.
Read more
Ce cours d'introduction aux probabilités a la même contenu que le cours de tronc commun de première année de l'École polytechnique donné par Sylvie Méléard.
Le cours introduit graduellement la notion de variable aléatoire et culmine avec la loi des grands nombres et le théorème de la limite centrale.
Les notions mathématiques nécessaires sont introduites au fil du cours et de nombreux exercices corrigés sont proposés.
Read more
Ce cours d'introduction aux probabilités a la même contenu que le cours de tronc commun de première année de l'École polytechnique donné par Sylvie Méléard.
Le cours introduit graduellement la notion de variable aléatoire et culmine avec la loi des grands nombres et le théorème de la limite centrale.
Les notions mathématiques nécessaires sont introduites au fil du cours et de nombreux exercices corrigés sont proposés.
Ce cours propose aussi une introduction aux méthodes de simulations des variables aléatoires comme la méthode de Monte Carlo. Des expériences numériques interactives sont également mises à votre disposition pour vous permettre de visualiser diverses notions.
Register for this course and see more details by visiting:
OpenCourser.com/course/0da522/aleatoire
What's inside
Syllabus
VECTEURS ALÉATOIRES (1/2)
Nous entamons cette semaine le Cours 4 dont le sujet est les vecteurs aléatoires, c'est-à-dire, une collection finie de variables aléatoires réelles, comme par exemple des couples de variables aléatoires. Ce cours s'étend sur deux semaines.
Read more
Syllabus
VECTEURS ALÉATOIRES (1/2)
Nous entamons cette semaine le Cours 4 dont le sujet est les vecteurs aléatoires, c'est-à-dire, une collection finie de variables aléatoires réelles, comme par exemple des couples de variables aléatoires. Ce cours s'étend sur deux semaines.
Read more
VECTEURS ALÉATOIRES (2/2)
Il s'agit de la suite et de la fin du Cours 4. Nous allons en particulier généraliser le résultat qui nous permet de faire des calculs de lois.
CONVERGENCES ET LOI DES GRANDS NOMBRES (1/2)
Nous entamons le Cours 5 dont l'objet principal est le théorème communément appelé la « loi des grands nombres ». Nous introduirons aussi plusieurs notions de convergence d'une suite de variables aléatoires.
CONVERGENCES ET LOI DES GRANDS NOMBRES (2/2)
Nous terminons le Cours 5 en donnant des exemples d'applications de la loi des grands nombres. Nous introduisons également la méthode de Monte Carlo.
FONCTIONS CARACTÉRISTIQUES, CONVERGENCE EN LOI ET THÉORÈME DE LA LIMITE CENTRALE (1/2)
Nous commençons le Cours 6, le dernier de ce MOOC, à cheval sur deux semaines. Cette semaine, on introduit un nouvel outil très puissant : les fonction caractéristiques.
FONCTIONS CARACTÉRISTIQUES, CONVERGENCE EN LOI ET THÉORÈME DE LA LIMITE CENTRALE (2/2)
Cette dernière semaine est consacrée au second pilier de la théorie des probabilités : le théorème de la limite centrale. Ce résultat nécessite une nouvelle notion de convergence : la convergence en loi. Nous verrons notamment une application aux intervalles de confiance qui sont utilisés pour les sondages.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Ce cours est une introduction aux probabilités permettant d'acquérir des fondements solides, car dispensé par des instructeurs réputés
Ce cours fournit une base pour les étudiants en mathématiques, en sciences, en ingénierie et dans d'autres domaines nécessitant une compréhension des probabilités
Ce cours est également précieux pour les étudiants en début de parcours souhaitant développer une compréhension approfondie des concepts fondamentaux de probabilité
Le cours couvre un éventail de sujets fondamentaux en probabilités, allant des vecteurs aléatoires à la loi des grands nombres
Le cours propose une introduction aux méthodes de simulation de variables aléatoires
Ce cours exige une familiarité préalable avec les mathématiques de base
Save this course
Save Aléatoire : une introduction aux probabilités - Partie 2 to your list so you can find it easily later:
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Reviews summary
Technical probabilities expanded
This is a graduate-level mathematics course giving a detailed and rigorous overview of the theoretical foundations of probability. It covers topics such as random variables, convergence, central limit theorems, and the law of large numbers. In particular, it covers vector calculus, probability functions, and Monte Carlo methods. It is a well-structured course with clear presentation and pacing delivered by a renowned professor with deep expertise in probability theory.
Interactive simulations help visualize concepts.
"Des expériences numériques interactives sont également mises à votre disposition pour vous permettre de visualiser diverses notions."
Course led by a well-respected professor.
"Le cours magistral y est très bien expliqué par Mme la professeure Sylvie Méléard"
Challenging exercises with detailed solutions.
"Les exercices corrigés sont très bien corrigés"
"très enrichissants, profonds d'explications dans l'ensemble"
A technical dive into probability theory.
"introduces advanced techniques such as function characteristics"
"very technical and focuses on proofs and in-depth explanations"
"le Théorème central limite expliqué dans la théorie de la Loi des grands nombres"
Lack of PDF support may be an inconvenience.
"il manque un support PDF"
Course may be too advanced for some or too basic for others.
"on ne sait pas pour qui ce cours est construit"
"je me suis retrouvé seul dans le forum"
Some mathematical maturity is expected.
"on introduit graduellement la notion de variable aléatoire et culmine avec la loi des grands nombres et le théorème de la limite centrale."
"avec notamment le fameux Théorème central limite expliqué dans la théorie de la Loi des grands nombres"
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Aléatoire : une introduction aux probabilités - Partie 2 with these
activities:
Review high school algebra and trigonometry concepts
Show steps
Reviewing these concepts will provide a strong foundation for understanding probability theory.
Browse courses on
Algebra
Show steps
-
Review the concepts of algebra and trigonometry
-
Solve practice problems to test your understanding
Organize notes, assignments, and practice problems
Show steps
Organization helps in recalling and reviewing course materials, improving knowledge retention.
Show steps
-
Gather all your course materials
-
Create a system for organizing your materials
-
Review your materials regularly
Watch video tutorials on probability theory
Show steps
Watching video tutorials is a good way to supplement the course material and ensure better understanding of complex concepts.
Browse courses on
Probability Theory
Show steps
-
Search for video tutorials on probability theory
-
Choose tutorials that cover the topics you are struggling with
-
Take notes while watching the tutorials
-
Review the tutorials regularly
Five other activities
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Show all eight activities
Form a study group with other students
Show steps
Collaboration with peers can provide different perspectives and enhance understanding through discussions.
Browse courses on
Probability
Show steps
-
Find other students taking the same course
-
Schedule regular study sessions
-
Discuss course material, solve problems, and prepare for exams together
Practice probability problems
Show steps
Repetition helps to solidify probability theory concepts.
Browse courses on
Probability
Show steps
-
Review the concepts of probability theory
-
Solve probability problems from textbooks or online resources
-
Participate in online forums or discussion groups to discuss probability problems
Create a probability cheat sheet
Show steps
Creating a cheat sheet requires recalling and summarizing important concepts, which aids in solidifying knowledge.
Browse courses on
Probability
Show steps
-
Gather information on probability theory formulas and concepts
-
Organize and summarize the information into a cheat sheet
-
Review the cheat sheet regularly
Write a blog post explaining a probability concept
Show steps
Writing about a concept helps internalize and reinforce understanding through explanation and organization of thoughts.
Browse courses on
Probability
Show steps
-
Choose a probability concept to write about
-
Research the concept thoroughly
-
Write a clear and concise explanation of the concept
-
Edit and proofread your blog post
Build a probability simulation model
Show steps
Building a simulation model challenges learners to apply probability theory to solve real-world problems.
Browse courses on
Probability
Show steps
-
Define the problem you want to simulate
-
Develop a probability model for the problem
-
Write a computer program to implement the simulation
-
Run the simulation and analyze the results
Review high school algebra and trigonometry concepts
Show steps
Reviewing these concepts will provide a strong foundation for understanding probability theory.
Browse courses on
Algebra
Show steps
Show steps
Show steps
- Review the concepts of algebra and trigonometry
- Solve practice problems to test your understanding
Organize notes, assignments, and practice problems
Show steps
Organization helps in recalling and reviewing course materials, improving knowledge retention.
Show steps
Show steps
Show steps
- Gather all your course materials
- Create a system for organizing your materials
- Review your materials regularly
Watch video tutorials on probability theory
Show steps
Watching video tutorials is a good way to supplement the course material and ensure better understanding of complex concepts.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Search for video tutorials on probability theory
- Choose tutorials that cover the topics you are struggling with
- Take notes while watching the tutorials
- Review the tutorials regularly
Five other activities
Expand to see all activities and additional details
Show all eight activities
Form a study group with other students
Show steps
Collaboration with peers can provide different perspectives and enhance understanding through discussions.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Find other students taking the same course
- Schedule regular study sessions
- Discuss course material, solve problems, and prepare for exams together
Practice probability problems
Show steps
Repetition helps to solidify probability theory concepts.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Review the concepts of probability theory
- Solve probability problems from textbooks or online resources
- Participate in online forums or discussion groups to discuss probability problems
Create a probability cheat sheet
Show steps
Creating a cheat sheet requires recalling and summarizing important concepts, which aids in solidifying knowledge.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Gather information on probability theory formulas and concepts
- Organize and summarize the information into a cheat sheet
- Review the cheat sheet regularly
Write a blog post explaining a probability concept
Show steps
Writing about a concept helps internalize and reinforce understanding through explanation and organization of thoughts.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Choose a probability concept to write about
- Research the concept thoroughly
- Write a clear and concise explanation of the concept
- Edit and proofread your blog post
Build a probability simulation model
Show steps
Building a simulation model challenges learners to apply probability theory to solve real-world problems.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Define the problem you want to simulate
- Develop a probability model for the problem
- Write a computer program to implement the simulation
- Run the simulation and analyze the results
Career center
Learners who complete Aléatoire : une introduction aux probabilités - Partie 2 will develop knowledge and skills
that may be useful to these careers:
Quantitative Researcher
Quantitative Researcher
Quantitative Researchers analyze data, build mathematical models and use statistical techniques to derive insights, primarily in the financial sector. They play a crucial role in developing and evaluating strategies for investment portfolios.
Data Scientist
Data Scientist
Data Scientists use their expertise in mathematics, statistics and probability to interpret and analyze complex datasets and extract valuable insights. They work on various projects, including developing and implementing predictive models, identifying trends and patterns, and optimizing business processes.
Machine Learning Scientist
Machine Learning Scientist
Machine Learning Scientists design, develop and implement Machine Learning models to solve complex problems, primarily in the field of computer science. They use their knowledge of probability theory and statistics to improve the performance and efficiency of these models.
Computational Statistician
Computational Statistician
Computational Statisticians use computational methods and tools to develop and implement statistical models and algorithms. They play a vital role in the research and development of new statistical methods and their applications in various fields.
Data Analyst
Data Analyst
Data analysts use their skills in statistics and programming to extract insights from data. They work in a variety of industries, including finance, healthcare, and retail. This course provides a strong foundation in probability theory, which is essential for understanding statistical methods. The course also covers topics such as data visualization and machine learning, which are used in a wide range of data analysis applications.
Machine Learning Engineer
Machine Learning Engineer
Machine learning engineers use their knowledge of statistics and computer science to develop and deploy machine learning models. They work in a variety of industries, including technology, finance, and healthcare. This course provides a strong foundation in probability theory, which is essential for understanding machine learning algorithms. The course also covers topics such as data mining and natural language processing, which are used in a wide range of machine learning applications.
Biostatistician
Biostatistician
Biostatisticians combine their knowledge of biology and statistics to design studies, collect and analyze data, and interpret results. They work in a variety of settings, including academia, industry, and government. This course provides a strong foundation in probability theory, which is essential for understanding statistical methods. The course also covers topics such as hypothesis testing and confidence intervals, which are used in a wide range of biostatistical applications.
Statistician
Statistician
Statisticians use their knowledge of mathematics and statistics to collect, analyze, and interpret data. They work in a variety of settings, including academia, industry, and government. This course provides a strong foundation in probability theory, which is essential for understanding statistical methods. The course also covers topics such as hypothesis testing and confidence intervals, which are used in a wide range of statistical applications.
Quantitative Analyst
Quantitative Analyst
Quantitative analysts use their knowledge of mathematics and statistics to develop and implement trading strategies. They work for investment banks, hedge funds, and proprietary trading firms. This course provides a strong foundation in probability theory, which is essential for understanding financial models. The course also covers topics such as risk management and portfolio optimization, which are used in a wide range of quantitative analysis applications.
Insurance Actuary
Insurance Actuary
Insurance actuaries use their knowledge of mathematics and statistics to assess risk and set insurance premiums. They work for insurance companies and consulting firms. This course provides a strong foundation in probability theory, which is essential for understanding actuarial models. The course also covers topics such as risk management and insurance pricing, which are used in a wide range of actuarial applications.
Underwriter
Underwriter
Underwriters use their knowledge of mathematics and statistics to assess risk and set insurance premiums. They work for insurance companies and consulting firms. This course provides a strong foundation in probability theory, which is essential for understanding actuarial models. The course also covers topics such as risk management and insurance pricing, which are used in a wide range of underwriting applications.
Risk Analyst
Risk Analyst
Risk analysts use their knowledge of mathematics and statistics to assess risk and make recommendations to clients. They work in a variety of settings, including financial institutions, insurance companies, and consulting firms. This course provides a strong foundation in probability theory, which is essential for understanding risk management models. The course also covers topics such as risk measurement and risk mitigation, which are used in a wide range of risk analysis applications.
Financial Analyst
Financial Analyst
Financial analysts use their knowledge of finance and statistics to evaluate investments and make recommendations to clients. They work in a variety of settings, including investment banks, hedge funds, and pension funds. This course provides a strong foundation in probability theory, which is essential for understanding financial models. The course also covers topics such as risk management and portfolio optimization, which are used in a wide range of financial analysis applications.
Teacher
Teacher
Teachers use their knowledge of mathematics and probability to teach students at the high school or college level. They work in a variety of settings, including public schools, private schools, and universities. This course provides a strong foundation in probability theory, which is essential for teaching probability concepts to students. The course also covers topics such as hypothesis testing and confidence intervals, which are used in a wide range of applications.
Operations Research Analyst
Operations Research Analyst
Operations research analysts use their knowledge of mathematics and statistics to solve complex problems in business and industry. They work in a variety of settings, including manufacturing, logistics, and healthcare. This course provides a strong foundation in probability theory, which is essential for understanding operations research models. The course also covers topics such as optimization and simulation, which are used in a wide range of operations research applications.
For more career information including salaries, visit:
OpenCourser.com/course/0da522/aleatoire
Reading list
We've selected 12 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Aléatoire : une introduction aux probabilités - Partie 2.
Ce livre est un manuel complet qui traite des probabilités et de la statistique. Il est particulièrement adapté aux élèves de première année de licence de mathématiques ou de physique.
Save
Comprehensive introduction to probability and mathematical statistics, with a focus on theory. It is written in a clear and concise style, and it includes numerous examples and exercises that help students to understand the material.
Save
Classic textbook on probability theory, with a focus on measure-theoretic foundations. It is written in a clear and concise style, and it includes numerous examples and exercises that help students to understand the material.
Provides a comprehensive introduction to probability theory, with a focus on applications in the sciences. It is written in a clear and concise style, and it includes numerous examples and exercises that help students to understand the material.
Graduate-level textbook on stochastic processes. It is written in a clear and concise style, and it includes numerous examples and exercises that help students to understand the material.
Save
Graduate-level textbook on Brownian motion. It is written in a clear and concise style, and it includes numerous examples and exercises that help students to understand the material.
Graduate-level textbook on measure theory and probability. It is written in a clear and concise style, and it includes numerous examples and exercises that help students to understand the material.
Graduate-level textbook on modern probability theory. It is written in a clear and concise style, and it includes numerous examples and exercises that help students to understand the material.
Classic textbook on probability and statistics, with a focus on applications in engineering and science. It is clearly written and provides a wealth of examples and exercises.
Provides a comprehensive introduction to probability theory, with a focus on applications in the social sciences. It is clearly written and provides a wealth of examples and exercises.
Ce livre aborde les probabilités et les statistiques d'un point de vue pratique, avec de nombreux exercices et applications. Il est particulièrement adapté aux étudiants en sciences souhaitant acquérir une base solide en matière de probabilités.
Cet ouvrage présente les concepts fondamentaux des probabilités et des statistiques de manière claire et concise. Il est particulièrement adapté aux étudiants en sciences et techniques souhaitant acquérir des connaissances de base en matière de probabilités.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/0da522/aleatoire
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Effort
2-3 hours/week
Via
Coursera
Institution
École Polytechnique
Instructors
Sylvie Méléard
Jean-René Chazottes
Carl Graham
Language
Français
Good to know
Ce cours est une introduction aux probabilités permettant d'acquérir des fondements solides, car dispensé par des instructeurs réputés
Ce cours fournit une base pour les étudiants en mathématiques, en sciences, en ingénierie et dans d'autres domaines nécessitant une compréhension des probabilités
Ce cours est également précieux pour les étudiants en début de parcours souhaitant développer une compréhension approfondie des concepts fondamentaux de probabilité
Le cours couvre un éventail de sujets fondamentaux en probabilités, allant des vecteurs aléatoires à la loi des grands nombres
Le cours propose une introduction aux méthodes de simulation de variables aléatoires
Ce cours exige une familiarité préalable avec les mathématiques de base
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