Academic Year 2018/2019
- Docente: Andrea Pascucci
- Credits: 9
- SSD: MAT/06
- Language: Italian
- Moduli: Andrea Pascucci (Modulo 1) Andrea Cosso (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Learning outcomes
At the end of the course, the student gets the basics of probability theory and statistical inference. He can apply this knowledge to scientific problems and applications where it is necessary to model random phenomena and conditions of uncertainty.
Course contents
Part 1. Measures and probability spaces. Discrete spaces and combinatorial calculation. Independence and conditioned probability. General spaces: distribution and distribution functions.
Part 2. Random variables and integration. Expected value and independence. Characteristic function.
Part 3. Expected value and conditional distribution.
Part 4. Sequences of random variables. Law of large numbers. Central limit theorem. Monte Carlo method.
Part 5. Introduction to Stochastic Processes: Poisson Process and Brownian Motion.
More details at
https://1drv.ms/w/s!AqFHqfUowiJljooHohq6ftBjgn8qHg
Readings/Bibliography
Notes and other material available at
https://www.dropbox.com/sh/ejjjj09g8c3wipb/AAAsuxl9pMyr_vKjCkbJTJEaa?dl=0
Teaching methods
Lectures (7 CFU) and tutorials (2 CFU).
Assessment methods
The exam consists of a written and an oral test.
The written test consists of 4 or 5 exercises (such as those left in class).
The oral exam covers the entire theoretical part and, if necessary, a brief discussion of the written exercises. For the preparation of the theoretical part, the lesson notes or the notes available in the didactic material together with the Mathematica codes of some examples are sufficient.
Teaching tools
See
https://www.dropbox.com/sh/ejjjj09g8c3wipb/AAAsuxl9pMyr_vKjCkbJTJEaa?dl=0
Links to further information
https://1drv.ms/w/s!AqFHqfUowiJljooHohq6ftBjgn8qHg
Office hours
See the website of Andrea Pascucci
See the website of Andrea Cosso