- 3MMPS2

Goal(s)

This course offers a deepening and extension of the concepts of probability calculus and statistical inference introduced in the course Probability and Statistics 1. The course follows an approach based on mathematical formalization.
The course is recommended for students interested in applied mathematics, financial engineering, and the foundations of data science and artificial intelligence.

Content(s)

• Axioms and basic definitions in probability, link with integration.
• Random variables and vectors, probability distributions.
• Conditioning, conditional expectation.
• Convergence of sequences of random variables, asymptotic theorems (strong law of large numbers, central limit theorem, etc.).
• Statistical estimation: estimation methods, quality and optimality of an estimator, quantity of information.
• Asymptotic results in statistics.
• In-depth study of hypothesis testing.
• Discrete-time random processes, Markov chains.
• Poisson processes.

Prerequisites are a basic knowledge of mathematics and probability, and the equivalent of the course Probability and Statistics 1.

The course uses notions of elementary measure theory and Lebesgue integrals from the Analysis and Calculus for Engineers course.