Instructor: Luigi Accardi
 

Elements of a probability space. Algebras of events and information about random experiments. Introduction to combinatorial calculus. Finite probability spaces, probability measures, introduction to Kolmogorov theory. Conditional probability, total probability formula, Bayes formula. Independent events. Random variables and their properties. Probability distribution, distribution function and densities function of a random variable. Inverse theorem. Expectation and variance of a random variable and their properties. Expectation and variance for the main kinds of random variables. Random vectors and their properties. Probability distribution, distribution functions and densities functions of a random vector. Independent random variables, covariance and correlation. Conditional expectation of a random variable and its properties. Conditional expectation as best estimator. Geometric approach to the conditional expectation. Sequences of random variables. Laws of large number. Central limit theorems.