The basics of probability theory and statistics

A.A. 2023/2024
6
Crediti massimi
56
Ore totali
SSD
ICAR/06 MAT/06 SECS-S/01
Lingua
Inglese
Obiettivi formativi
The course unit focuses on the basic elements of probability, estimation theory and hypothesis testing. Particularly, the Least Squares method and the related hypothesis testing will be discussed in some details.
Risultati apprendimento attesi
The students attending this course unit are expected to acquire the basic concepts of probability and statistics. This is obtained by giving them the key points of the axiomatic theory of probability and some relevant numerical applications of the theory.
Corso singolo

Questo insegnamento può essere seguito come corso singolo.

Programma e organizzazione didattica

Edizione unica

Responsabile
Periodo
Secondo semestre

Programma
Probability according to Laplace and Von Mises. The axiomatic definition of probability. Sample space and event space. Basic theorems on probability. Conditional probability and stochastic independence of events.
Random variables in one dimension. The cumulative distribution function. Mean and variance. The Chebyshev inequality. The two-dimensional random variables: joint and marginal distributions, mean, variance and covariance, linear correlation coefficients. The n-dimensional random variable (basics).
Distribution of functions of random variables. The expectation theorem. Covariance propagation.
Sequences of random variables. The Bernoulli theorem. The central limit theorem
Populations and samples. The histogram. Statistical Inference and Maximum Likelihood. Unbiased and consistent estimators. Sample mean and sample variance. Least Squares. Tests of hypotheses. Tests of hypotheses on Least Squares Estimators.
Prerequisiti
Calculus and Linear Algebra.
Metodi didattici
Mixture of direct instruction and flipped classroom.
Materiale di riferimento
Mood A.M., Graybill F.A. and Boes D.C., Introduction to the theory of statistics. Mc Graw-Hill, 1974, ISBN: 0-07-042864-6
Papoulis A., Pillai S. U., Probability, random variables and stochastic processes. Mc Graw-Hill, 2002, ISBN: 0-07-366011-6
Cramer H., Mathematical methods of statistics. Princeton University Press, 1957
Modalità di verifica dell’apprendimento e criteri di valutazione
L'esame finale consiste in un orale sugli argomenti svolti in classe. Il voto verrà stabilito sulla base dei seguenti criteri: conoscenza dei temi trattati nelle lezioni frontali; capacità di ragionamento critico; capacità di usare un lessico specifico della materia trattata; analisi di specifici modelli probabilistici.
Il punteggio finale sarà espresso in trentesimi.
ICAR/06 - TOPOGRAFIA E CARTOGRAFIA
MAT/06 - PROBABILITA E STATISTICA MATEMATICA
SECS-S/01 - STATISTICA
Esercitazioni pratiche con elementi di teoria: 24 ore
Lezioni: 32 ore
Docente/i