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.
Assessment methods and criteria
The learning is checked step by step by written intermediate tests.
The final written test will check the technical and conceptual skill of the student and his mastership facing various problems which involve variations on previously discussed exercises.
Other information
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