CALCOLO DELLE PROBABILITA’ E STATISTICA

Anno accademico 2020-2021

CALCOLO DELLE PROBABILITA' E STATISTICA

Docenti:
Luigi Pace
Anno di corso: 2
Totale crediti: 6
Tipologia: Affine/Integrativa
Periodo didattico: Primo Periodo
Prerequisiti. A good working knowledge of Calculus is required.
Metodi didattici. Frontal lectures.
Modalità di verifica. Questions in the written exam are in Italian. Erasmus students may write their answers in English, French or Spanish.

OBIETTIVI FORMATIVI

The student should acquire basic notions of: probability and conditional probability (Bayes’ theorem); random variables (with secure distinction between discrete and continuous distributions); expectation, variance, and further moments, being also able to use the moment generating function; the main univariate probability distributions; the modes of convergence of sequences of random variables (and limit theorems); the usual procedures of statistical inference in the simples models of random sampling.

The student should be able to use the main results of probability in order to: solve simple problems on probabilities an conditional probabilities; chose probability distributions apt to describe a random phenomenon; appropriately use approximate probability distributions, even for inference.

The student should be able to model simple situations of uncertainty.

 

The student should be able to discuss the reasons leading to a particular stochastic model in simple uncertainty situations and to explain in an adeguate manner the conclusions of a statistical inference.

The student should be able to deepen her knowledge in probability and statistical inference, practicing analysis of data from databases, for instance in view of cybersecurity.

CONTENUTI

This course gives an elementary introduction to Probability with a view towards

Statistics. The main topics are

1. Elementary probability

2. Random variables, unidimensional and multidimensional, discrete and continuous

3. Moments and moment generating function

4. Special univariate distributions

5. Modes of convergence, LLN and CLT

6. Introduction to statistical inference

TESTI DI RIFERIMENTO

P.Baldi, Calcolo delle probabilità e statistica 
(seconda edizione), McGraw-Hill, Milano, 1998.