This course is dedidcet to introduce basic concepts in Probability Theory. the aim is to give a solid background and the instrumentes to understand the probabilistic language: the student shound be able to build and analyse easy stochastic models. The links with other disciplines as Analysis and Statistics will be presented.
Introduction to modeling of random phenomena.
Introduction of probability: assiomatic costruction of probabiloty spaces. Concept of independence, conditional probability. Bayes Theorem. Random variables: distribution function, expectation, variance (Bernoulli, Binomiale, Geometrica, Binomiale Negativa, Ipergeometrica, Normale, Uniforme, Cauchy, Esponenziale, Gamma, Chi-Quadro, t di Student,...). Markov and Chebychev inequalities. Random vectors. Characteristic functions. Convergence definitions and theorems. Law of large numbers and Central limit theorem. Stochastic simulation.
K. L. Chung, A Course in probability Theory
J. Jacod, P. Protter, Probability Essentials
Ricevimento: By appointment by email.
Ricevimento: Thursday: 14.00-15.30, office 836, or by arrangement made by email.
EMANUELA SASSO (President)
ERNESTO DE VITO
VERONICA UMANITA' (President Substitute)
The class will start according to the academic calendar.
The exam consists of a written test and an oral exam.
