Probability Theory

To illustrate, from a probabilistic perspective, the concepts covered in the “Measure—Integration—Fourier” course unit, and to introduce the necessary tools for students who will take the Stochastic Modeling course unit in the second semester of their third year of undergraduate studies. 

This lesson will cover the following topics:

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

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

- Law of large numbers: the 0-1 law, almost certain convergence, and convergence 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 courses on analysis and probability in the first and second years, specifically:

- HAX304X Probability

Recommended prerequisites: L2 Math

Hourly volumes:

            CM: 18

            TD: 18

            Practical Work: -

            Land: -