Elementary probability theory: discrete distributions, repeated trials, continuous random variables. Some basic limit theorems and introduction to Markov chains.
Curriculum
teacher profile teaching materials
- F. Caravenna e P. Dai Pra, Probabilita' (Springer Ed.)
- W. Feller, An introduction to probability theory and its applications (Wiley, 1968).
Programme
Combinatorics, assioms of probability, conditional probability and independence, discrete random variables. Continuous random variables, density and distribution functions. Independence and joint laws. Relation between exponential distribution and Poisson distribution. Limit theorems, moment generating functions and sketch of central limit theorem.Core Documentation
- S. Ross, Calcolo delle probabilita' (Apogeo Ed.)- F. Caravenna e P. Dai Pra, Probabilita' (Springer Ed.)
- W. Feller, An introduction to probability theory and its applications (Wiley, 1968).
Reference Bibliography
- S. Ross, Calcolo delle probabilita' (Apogeo Ed.) - F. Caravenna e P. Dai Pra, Probabilita' (Springer Ed.) - W. Feller, An introduction to probability theory and its applications (Wiley, 1968).Type of evaluation
The written part mainly consists of exercises, but there can be questions about the theoretical parts seen in class (check with the lecturer for further details). teacher profile teaching materials
- F. Caravenna e P. Dai Pra, Probabilita' (Springer Ed.)
- W. Feller, An introduction to probability theory and its applications (Wiley, 1968).
Programme
Combinatorics, assioms of probability, conditional probability and independence, discrete random variables. Continuous random variables, density and distribution functions. Independence and joint laws. Relation between exponential distribution and Poisson distribution. Limit theorems, moment generating functions and sketch of central limit theorem.Core Documentation
- S. Ross, Calcolo delle probabilita' (Apogeo Ed.)- F. Caravenna e P. Dai Pra, Probabilita' (Springer Ed.)
- W. Feller, An introduction to probability theory and its applications (Wiley, 1968).
Reference Bibliography
- S. Ross, Calcolo delle probabilita' (Apogeo Ed.) - F. Caravenna e P. Dai Pra, Probabilita' (Springer Ed.) - W. Feller, An introduction to probability theory and its applications (Wiley, 1968).Type of evaluation
The written part mainly consists of exercises, but there can be questions about the theoretical parts seen in class (check with the lecturer for further details).