Probability Theory

Illustrate the concepts covered in the "Measurement - Integration - Fourier" course from a probabilistic perspective, and introduce the necessary tools to students who will be taking the Stochastic Modeling course in the second semester of their junior year. 

This EU will address the following points:

- Probabilistic modeling: Probability space, probability distribution, Bayes' theorem, independence of events and tribes

- Random variables: definition, examples, common distributions, independence. Distribution function for random variables and vectors. Expectation. Characteristic function.

- Law of large numbers: law of 0-1, almost certain convergence and in probability. Application to point estimation.

- Central Limit Theorem: convergence in distribution, comparison with other types of convergence. Application of the central limit theorem to interval estimation.

The L1 and L2 analysis and probability courses, in particular:

- HAX304X Probability

 

Recommended prerequisites: L2 maths

Hourly volumes:

            CM: 18

            TD: 18

            TP: -

            Land: -