# PROBABILITY METHODS IN PHYSICS

## Learning outcomes of the course unit

To get familiarity with the basic mathematical formalism of probability theory, with applications in Physics, Information Theory and Statistics.

## Prerequisites

Basic courses in calculus and algebra.

## Course contents summary

Probability spaces, elementary events, conditional pobability, Bayes formula, independence.

Combinatorial analysis, Bernoulli processes. Chebyshev inequality.

Distributions and partition function. Binomial distribution.

Discrete random variables, variance and expectation. Independence. Covariance.

Exponential, uniform and normal densities.

Various random variables. Continuous random variables.

Functions of random variables.

Algorithms and sequences.

Central limit theorem. Samples and confindence intervals.

Markov chains, classification of states, ergodic chains.

Information and entropy, partitions formalism.

## Course contents

Probability spaces, elementary events, conditional pobability, Bayes formula, independence.

Combinatorial analysis, Bernoulli processes. Chebyshev inequality.

Distributions and partition function. Binomial distribution.

Discrete random variables, variance and expectation. Independence. Covariance.

Exponential, uniform and normal densities.

Various random variables. Continuous random variables.

Functions of random variables.

Algorithms and sequences.

Central limit theorem. Samples and confindence intervals.

Markov chains, classification of states, ergodic chains.

Information and entropy, partitions formalism.

## Recommended readings

Giovanni Cicuta, Lezioni ed esercizi 2011-12.

G Boffetta e A. Vulpiani, Probabilità in Fisica (Springer 2012)

K. Baclawski and G-C Rota, An Introduction to Probability and Random Processes (typed notes online)

M. Verri, Probabilità & Statistica (Esculapio 2008)

## Teaching methods

Lessons and exercises in the classroom.

## Assessment methods and criteria

The learning is checked by written tests.

Such tests will check the technical and conceptual skill of the student facing various problems which involve variations on previously discussed exercises.