37529 - Mathematical Probability and Statistics 1

Learning outcomes

At the end of the course, students know the basics of probability theory and statistical inference. They know how to apply this knowledge to scientific problems and applications where it is necessary to model random phenomena and uncertainty conditions.

Course contents

The complete program is available here.

In summary:
Part 1. Measures and probability spaces. Discrete spaces and combinatorics. Independence and conditional probability. General spaces: distributions and distribution functions.
Part 2. Random variables and integration. Expected value and independence. Characteristic function.
Part 3. Expectation and conditional distribution.
Part 4. Sequences of random variables. Law of large numbers. Central limit theorem. Monte Carlo method.

More details at the webpage.

Readings/Bibliography

A. Pascucci, “Teoria della Probabilità”, Springer 2020

Teaching methods

Frontal lessons (7 CFU) and exercises (2 CFU).

Assessment methods

The exam consists of a written and an oral test.

The written test remains valid for all subsequent oral appeals: if the written test is taken several times, it is considered the one with the highest grade.

The written exam consists of 4 or 5 exercises.

The oral part covers the whole theoretical part and possibly a brief discussion of the written exercises. For the preparation of the theoretical part the lesson notes are sufficient.

Teaching tools

At the website the following material is available:

- notes for the course;
- Mathematica files with numerical examples;
- exercise sheets and old examss solved.

The Mathematica reader can be downloaded free of charge from
http://demonstrations.wolfram.com/download-cdf-player.html

Links to further information

https://1drv.ms/w/s!AqFHqfUowiJlkJ94lxdKq_yCGO1mpg?e=PDSSPe

Office hours

See the website of Andrea Pascucci

See the website of Antonello Pesce