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

Events and probability: probability spaces, conditional probabilities, Bayes theorem. 
Discrete random variables: probability mass functions, examples of random variables, expectation and variance, bivariate discrete distributions.
Independence of random variables, sums of random variables, indicator functions.
Continuous random variables: density and distribution functions, examples of continuous random variables, expectation and variance. The Gaussian distribution and properties.
Functions of discrete and continous random variables.

Readings/Bibliography

Lecture notes

Probability, an Introduction, G. Grimmett & D. Welsh, (2014), Oxford University Press: chapters 1,2,3,5.

Teaching methods

Lectures and tutorials

Assessment methods

The learning assessment is composed by a written test lasting 2 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 Cinzia Viroli