This course provides an introduction to probability theory. Its purpose is to equip students with the concepts and methods required to model and analyse random phenomena. It covers the basic principles of combinatorics and probability, conditional probability and independence, as well as discrete and continuous random variables and their main characteristics. It also introduces the probability distributions most commonly used in statistics and econometrics.
- Enseignant éditeur: Brochard Delphine
- Enseignant éditeur: Defebvre Eric
This course is designed for second-year undergraduate students in Economics. Its aim is to demonstrate the relevance and importance of probability theory for the analysis of socio-economic data. Particular emphasis is placed on understanding the concepts introduced and the conditions under which they can be applied.
More specifically, by the end of the course, students should be able to:
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understand the concepts of random experiments, events, random variables and probability distributions;
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model a random experiment and calculate the associated probabilities;
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identify the main standard probability distributions and use them to model random phenomena;
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understand the concepts of independence, statistical dependence and correlation;
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present their reasoning clearly and provide rigorous justification for each step of their mathematical arguments.
One of the main objectives of the course is to provide students with the foundations in probability theory required to study statistics and econometrics in the third year of the undergraduate programme.
The main topics covered are:
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Foundations of probability: sample spaces, events, elementary probabilities, fundamental properties of probability, and applications to discrete sample spaces.
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Conditional probability and independence: conditional probabilities, the law of total probability, Bayes’ theorem, and independence.
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Random variables: definition of a random variable, probability distributions, real-valued random variables, cumulative distribution functions, and functions of random variables.
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Discrete random variables: discrete numerical random variables, moments, and standard discrete probability distributions.
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Absolutely continuous random variables: continuous cumulative distribution functions, probability density functions, moments, and standard continuous probability distributions.
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Pairs of discrete random variables: joint and marginal distributions, covariance, correlation, and conditional distributions.
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Pairs and sequences of random variables
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The Central Limit Theorem
No prior knowledge of probability theory is required. However, students are expected to be comfortable with the basic mathematical tools covered in secondary school and during the first year of the undergraduate programme. These include algebraic manipulation, equations and inequalities, elementary functions, finite sums and products, exponentials and logarithms, and basic differentiation and integration.
The necessary mathematical preliminaries are reviewed in Worksheet 0, which must be completed before the first tutorial session.
Two ungraded mock tests will be organised during tutorial sessions:
- One halfway through the semester, during Session 5
- One at the end of the semester, during Session 12
Particular importance will be placed on mastering the concepts, reasoning and mathematical writing.
The final examination will take place in January and will last two hours.
