68357 - Laboratory In Probability

Course Unit Page

Academic Year 2018/2019

Learning outcomes

At the end of this course the student knows the concept of probability space, how to use logical operators to derive complex events, the main features of combinatorics and the essential rules of elementary probability, including conditional probability. Therefore, the student is able to solve a wide selection of exercises regarding simple and conditional probability.

Course contents

Sets and set operations. Sigma algebras. Probability.

Some theorems on probabilities. Conditional probability and

independence. Random variables. Distribution functions.

Discrete and absolutely continuous r.vs.. Density functions.

Examples. Moments of r.vs.. Multivariate r.vs., independence,

correlation and joint distributions (and densities). Transformations

of r.vs. and computation of their distributions.

Readings/Bibliography

Jacod - Protter: "Probability Essentials"

Chow - Teicher: "Probability Theory: Independence, Interchangeability,

Martingales"

Billingsley: "Probability and Measure"

Teaching methods

Frontal lessons

Assessment methods

No final exam

Teaching tools

None

Office hours

See the website of Fabio Gobbi