30546 - PROBABILITY
Course taught in English
Go to class group/s: 27
Lezioni della classe erogate in presenza
Set theory. Sequences and series. Continuous and differentiable functions. Integrals. Complex numbers.
Probability is the language of uncertainty. It is essential to express inherent stochasticity of the world, to describe information and lack of knowledge and to make predictions. For this reason it is the bedrock of machine learning and artificial intelligence. You cannot develop a deep understanding and application of artificial intelligence without it. The course will provide a rigorous introduction to probability. Students will gain a solid grounding on the its foundations, will learn how to deal with randomness with the correct mathematical tools and how to solve problems.
• Probability spaces
• Random variables and random vectors
• Expectation and integral transforms
• Simulation of random variables
• The simple random walk
• Modes of convergence for sequences of random variables
• Conditional expectation and prediction
- recognize appropriate models to describe a random environment;
- identify the correct methodology for solving problems under uncertainty;
- discuss the role of the assumptions in a probabilistic model
- understand the mathematical proofs and dicuss the role of the hypotheses.
- translate a problem into the language of probability;
- apply the probabilistic techniques to solve problems involving uncertainty;
- interpret the solutions derived from implementing the chosen model;
- develop autonomously simple mathematical proofs.
- Face-to-face lectures
- Exercises (exercises, database, software etc.)
- Individual assignments
Exercises will be proposed to students and their solution will be discussed in class.
Individual assignment will be proposed by Blackboard tools for training and self assessment.
Assessment, both for attending and non-attending students, is based on continuous assessment (20%) and partial exams or general exam (80%).
Continuous assessments are made of multiple choice and numerical questions. The aim is verifying:
- the ability to recognize appropriate models for a random environment
- the ability to apply the correct techniques to solve problems.
Partial and general exams are made of theoretical and numerical questions. The aim is verifying:
- the ability to develop autonomously simple mathematical proofs and discuss the role of the assumptions
- the abillity to solve problems and interpret the solutions.
Grimmett, G.R. & Stirzaker, D.R. (2001). Probability and Random Processes. Oxford University Press.