LEARNING OUTCOMES

Introduction to modeling of random phenomena.

SYLLABUS/CONTENT

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.

RECOMMENDED READING/BIBLIOGRAPHY

K. L. Chung, A Course in probability Theory

J. Jacod, P. Protter, Probability Essentials

Exam Board

EMANUELA SASSO (President)

ERNESTO DE VITO

VERONICA UMANITA' (President Substitute)

LESSONS START

The class will start according to the academic calendar.

Exam description

The exam consists of a written test and an oral exam.

Exam schedule