79222 - Probability I

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 and compute their expected values and variances - analytically treat univariate and bivarate random variables.

Course contents

Discrete probability spaces, conditional probability, law of total probability, Bayes' formula, independent events. Discrete random variables, probability function, joint probability function, independent random variables, expected value, variance, covariance. Models of discrete random variables: Bernoulli, Binomial, Poisson, Geometric.

General probability spaces, random variables, distribution function, independent random variables, continuous random variables, probability density function, expected value, variance and covariance for continuous random variables. Models of continuous random variables: Uniform, Gaussian, Gamma, Student and Fisher.

Law of large numbers and Central Limit theorem.

Readings/Bibliography

Lecture notes

Teaching methods

Lectures and tutorials

Assessment methods

The learning assessment is composed by a written test lasting one hours, followed by an oral examination. The written test is aimed at assessing the student's ability to use the definitions, properties and theorems of probability theory in solving theoretical exercises. During the written exam, students can make use of a formulary and a calculator. The written test consists of some exercises articulated in several points with a final grade out of thirty. 

Office hours

See the website of Alberto Lanconelli