Probability, 1st year ENPC

- Course coordinator: Julien Guyon (ENPC). - Teaching team: Hervé Andrès, Dimitri Daucher, Jean-François Delmas, Anne Dutfoy, Julien Guyon, Paul Invernizzi, Benjamin Jourdain, Alain Toubol. - Course description: The aim of this course is to provide engineers with essential knowledge in probability. We will present fundamental concepts (probability space, random variable, distribution, expected value, etc.) as well as common probability distributions. Emphasis will be placed on the tools for characterizing and calculating these distributions. We will introduce the various concepts of convergence to ensure a thorough understanding of the two fundamental theorems: the strong law of large numbers and the central limit theorem. Finally, we will address a more numerical and practical aspect by presenting the main algorithms for simulating random variables and introducing the Monte Carlo method. - Course curriculum. - Validation requirements for students: see Educnet. Course materials: - Lecture notes. Those lecture notes have been published under the title Probabilités et statistique, Ellipses, 2009. - Complements on measure theory and integration theory (probability space, random variables, probability measure, distribution of a random variable, expectation). - Week 1: Optional homework assignment. - Week 4: Exercises on the convergence of sequences of random variables (by Aurélien Alfonsi). - Week 5: A required homework assignment on the Monte Carlo method will be posted here. - Week 6: A simulation exercise using Python, to test the random number generator and illustrate the convergences in the strong law of large numbers and the central limit theorem, will be posted here.