00082 - Probability Theory

Learning outcomes

By the end of the module the student knows the basic tools of probability calculus with particular reference to their role for statistical analysis. In particular, the student is able to calculate the probability of complex events, using the fundamental axioms and theorems of the calculus of probability together with the main mathematical models for 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/One and a half-hour written exam, articulated in a series of two/three exercises each with a maximum grade of 10/15 points. Every exercise attains to elements of the syllabus covered during the course lectures.

The overall grade for the integrated course takes into account the outcome of the two modules (Statistics + Probability Theory) and is expressed in thirtieths.

For the part of the exam related to Statistics, please refer to Guideweb for that subject.

In case of online exams, 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