- Docente: Lorenzo Torricelli
- Credits: 6
- SSD: MAT/06
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Statistics, Economics and Business (cod. 6811)
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from Sep 17, 2025 to Oct 22, 2025
Learning outcomes
At the end of the course, the student will know the basic tools of probability theory, with particular emphasis on their role in statistical analysis. In particular, the student will be able to: determine the probability of a random event using the axioms and fundamental theorems of probability theory, and handle the main discrete and continuous random variables.
Course contents
- Probability spaces and Kolmogorov’s axioms
- Conditional probability, Law of Total Probability, and Bayes' Theorem. Monotonicity and limit theorems.
- Independent events
- Random variables and distribution functions, discrete and continuous random variables, expected value, variance, and covariance, inequalities
- Discrete random variables: Bernoulli, Binomial, Hypergeometric, Poisson, Geometric
- Continuous rnadom variables: Uniform, Gaussian, Log-normal, Gamma, Student's T
- Law of Large Numbers and applications
- Central Limit Theorem and applications
Readings/Bibliography
- Alberto Lanconelli, Introduzione alla Teoria della Probabilità (2023) ISBN-13 : 979-8852499196
- Paolo Baldi, Calcolo delle probabilità e Statistica, McGraw Hill
Teaching methods
Classroom lectures
Assessment methods
Written exam lasting 90, four or five theoretical and practical questions. Any total score exceeding 31 results in honors (lode) being awarded. Oral interviews complementing the exam are possible.
Teaching tools
Chalk and Blackboard
Office hours
See the website of Lorenzo Torricelli