Laura Poggiolini Note di Calcolo delle Probabilità. Pitagora Editrice.
Notes to be doenloaded from the web (will be made available during the course)
Learning Objectives
Introduction to methods and results of probability and statistics
Prerequisites
Topics from the courses Analisi Matematica I e II, Geometria e Algebra lineare
Teaching Methods
Classes
Type of Assessment
The exam is divided:
in a written part whose objective is the capability of applying the topics of the course to simple examples e the knowledge of the main results of the subject;
in an oral part whose obective is to verify the theoretical knowledge of the topics of the course
Course program
Elements of probability theory: probability spaces, random variables, expected value, variance, moments. Some examples of random variables: binomial, Poisson, Gaussian r.v. Conditional probability, Bayes theorem, independence of events and of random variables. Conditional expectation. Markov and Chebychev inequalities. Large number theorems, Central Limit Theorem.
Measure theory: Lebesgue measure, Lebesgue integral. abstract measures and probability measures. An introduction to stochastic processes: covariance and correlation. Martingales and Brownian motion.
Topics from statistics: sampling, confidence intervals, Statistical hypothesis testing, consistent estimators, non-bias estimators. Estimators of sample mean and sample variance. Student's t distribution, chi-square distribution, Pearson's chi-squared test. Regression, maximal likelihood.