32827 - Theory of Probability

Course Unit Page

Academic Year 2018/2019

Learning outcomes

At the end of the course, the candidate will be able to apply the basic tools of probability, especially the most useful within statistical analysis. Specifically, he will be able to calculate the probability of complex events, to manage a wide range of  discrete and continuous random variables, and to know and apply the main discrete random process patterns.

Course contents

Events and logical operations. Combinatorics. Axioms and elementary probability. Conditional probability and Bayes theorem. Discrete random variables and related models (Binomial, Geometric, Hypergeometric, Pascal, Poisson). Continuous random variables and related models  (Uniform, Exponential, Gamma and Beta). Gaussian variables and derived distributions (Log-normal, Chi squared, Student t-distribution, Snedecor-Fisher F-distribution). Pareto Distribution. Bivariate discrete random variables. Covariance and its properties. Sequences and convergences of random variables. Bernoulli Theorem and Central Limit Theorem. Graduation function. Ordinal variables. Moment-generating function. Discrete Random Processes. Random walks. Poisson Processes with applications. Markov chains. Definition of martingale process and brownian motion.

Readings/Bibliography

Maurizio Brizzi. Calcolo delle probabilità con note introduttive di inferenza statistica. Editrice Lo Scarabeo, Bologna,  2004 (only in Italian)
Maurizio Brizzi. Introduzione al calcolo delle probabilità e all'inferenza statistica. Libreriauniversitaria.it, Limena (PD), 2014 (only in Italian)
Geoffrey Grimmett and David Stirzaker. Probability and Random processes. Oxford University Press, 2001.

Teaching methods

Direct teaching and at least 4-6 hours of laboratory work.

Assessment methods

Written test including three  exercises with numerical applications. Each exercise can be valued between 9 and 12 points. Oral test concerning theory and quick numerical examples.

Teaching tools

Working sheets containing theoretical features and exercises will be available to students (even in English).

Office hours

See the website of Maurizio Brizzi