Giuseppe MODICA, Laura POGGIOLINI - Note di calcolo delle probabilità - seconda edizione, 2013, Pitagora.
Notes to be downloaded from the web (they will be made available during the course)
Learning Objectives
Present some mathematical instruments for the description of stochastic phenomena
Prerequisites
The topics in the courses:
Analisi Matematica I,
Analisi Matematica II e Probabilità,
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;
in an oral part whose obective is to verify the theoretical knowledge of the topics of the course
Course program
Jordan matrices and Jordan canonical form. Spectral theorem. Variation characterization of the eigenvalues of selfadjoint operators.
Weak and strong law of great numbers. The Central Limit Theorem. Stochastic vectors and stochastic matrices. Markov chains.
Elements of descriptive statistics: individuals, population, characters. Sampling. Mode, median, mean, variance. Bivariate samples: covariance, linear and logistic regression. Principal components analysis.
Inferential statistics:
Statistic sample, Campione statistico. Statistics. Sample mean and sample variance. Likelihood estimators. Bayesan estimators. Distribution of the sample mean of a Bernoulli sample. Chi-square, Student's t distributions and their relations with Gaussian samples. Confidence interval. Statistical hypothesis testing. Statistical hypothesis testing for discrete densities.