# 37529 - Mathematical Probability and Statistics 1

## 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

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