Probability & Measure

This course covers the basics of probability theory from a measure-theoretic perspective. We start with the concept of probability spaces and the formal definitions of random variables and independence. We then introduce the measure integral and its key properties. Afterwards, we explore different types of convergence for random variables and provide proofs of the law of large numbers and the central limit theorem. The course concludes with a brief introduction to stochastic processes.

1. Learn the fundamental concepts, results and models in probability theory. 
2. Develop the ability to mathematically describe and analyze random phenomena.
3. Understand and apply the key limit theorems for sequences of independent random variables.
4. Build a solid foundation for further study in statistics and stochastic processes.

In presenza

1. Weekly lectures (2hrs)
2. Weekly tutorials (2hrs)

Exercises (40%)
Final (60%)