30546 - PROBABILITY
Department of Decision Sciences
Course taught in English
Go to class group/s: 27
Course Director:
SANDRA FORTINI
SANDRA FORTINI
Suggested background knowledge
Set theory. Sequences and series. Continuous and differentiable functions. Integrals.
Mission & Content Summary
MISSION
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.
CONTENT SUMMARY
- Probability: definition and properties
- Conditional probability and independence
- Random variables and random vectors
- Joint and conditional distributions
- Expectation and moments
- Integral transforms
- Convergence in distribution and the Central Limit Theorem
- Modes of convergence and the laws of large numbers
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
- 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.
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
- 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.
Teaching methods
- Lectures
- Practical Exercises
- Individual works / Assignments
DETAILS
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 methods
| Continuous assessment | Partial exams | General exam | |
|---|---|---|---|
|
x | x | |
|
x |
ATTENDING AND NOT ATTENDING STUDENTS
Assessment, both for attending and non-attending students, is based on continuous assessment (15%) and partial exams or general exam (85%).
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.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
Fortini, S. Gaffi, F. Introduction to Probability. BAI 30546. BAI series, Volume 2, Academic Year 2024, Egea
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