30216 - Probability Models

Course Unit Page

Academic Year 2018/2019

Learning outcomes

At the end of the course the student knows some advanced probability theories with application to computer science, such as Markov chains with discrete and continuous time. He is able to analyze some simple stochastic systems such some with application to biology.

Course contents

Denumerable additivity. One-dimensional random walk. Generating function. Gamblers' ruin problem. Galton Watson processes. Markov chains. Recurrent and transient states. Stationary distributions. Reversible Markov chains.  Gibbs sampler. Metropolis algorithm. Markov chains with continuous time. Poisson process. Pure birth processes. Semi-Markov processes. Queueing processes. Queueing Markov processes.. Open and closed systems of queues. Jackson's property.

Readings/Bibliography

S. Ross. Introduction to Probability Models. Academic Press.
W. Feller.An Introduction to Probability Theory and Its Applications. I Vol.. Wiley.

Teaching methods

Lectures.

Assessment methods

Final verification consists in an oral test.

Oral test consists in a talk, starting from three questions, with the goal of testing the understanding of the basic concepts of the course, the ability of solving simple exercises and of developing  logical arguments.

 

Teaching tools

Lectures.

The course is based on lectures in which a series of probability models that are relevant for applications to computer science will be illustrated with examples of their applications and the development of simple exercises in order to familiarize  students with concrete application of the introduced mathematical models.

 

 

 

 

Office hours

See the website of Massimo Campanino