84608 - Probability

Learning outcomes

By the end of the course module the student should know the basic tools of probability calculus, with a special focus on their role in the statistical analysis. In particular, the student should be able to: - compute the probability of events, by using the axioms and the fundamental theorems of probability calculus - identify the main discrete and continuous random variables

Course contents

• Probability spaces and Kolmogorov axioms
  
• Conditional probability, Law of Total Probability and Bayes' formula
• Independent events
  
• Random variables and distribution functions, discrete and continuous random variables, expected value, variance and covariance
  
• Discrete models: Bernoulli, Binomial, Hypergeometric, Poisson, Geometric
• Continuous models: Uniform, Gaussian, Gamma, Student, Fisher.
  
• 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.
  

Teaching methods

Lectures and tutorials

Assessment methods

One-hour written exam, articulated in a series of 2 exercises each with a maximum grade of 15 points. The possible award of "lode" is conditional on the mathematical rigour demonstrated in the solution of the exercises. Every exercise attains to elements of the syllabus covered during the course lectures. In case of online exam, this will be supported by the softwares Teams, Zoom and EOL (https://eol.unibo.it/)

Teaching tools

Exercises with solutions

Office hours

See the website of Alberto Lanconelli