# PROBABILITY METHODS IN PHYSICS cod. 13610

3° year of course - Second semester
Professor
Fisica teorica, modelli e metodi matematici (FIS/02)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in - - -

## Learning objectives

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 unit content

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.

## Full programme

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.

## Bibliography

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.

oral exam

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