84608 - Probability

Academic Year 2025/2026

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Statistics, Economics and Business (cod. 6811)

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 90–120 minutes, with a variable number of exercises. Any total score exceeding 31 results in honors (lode) being awarded.

Teaching tools

Chalk and Blackboard

 

Office hours

See the website of Lorenzo Torricelli