Course Details for A.Y. 2018/2019

The information on this page refer to the academic year 2018/2019. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2018/2019

Name:

Calcolo delle Probabilità e Statistica Matematica / Probability And Mathematical Statistics

Type:

Course

Basic information

Code:

DT0003

Sector:

MAT/06

Credits:

: Bachelor Degree in Computer Science 6 CFU (c)

Term:

1^st semester

Degree(s):

Bachelor Degree in Computer Science 2^nd anno curriculum General Compulsory

Language:

Italian

Teacher(s):

Davide Gabrielli
Umberto Triacca

Propaedeutics:

Mathematical Analysis

Course Objectives

An introduction to the theory of probability up to the weak law of large numbers

Course Content

BASIC PROBABILITY: probability space, sets and elementary operations, Venn diagragms, basic axioms, inclusion-exclusion formula, enumeration principle and generalized enumeration principle, uniform probability spaces, permutations and combinations, conditional probability, disintegration formula, Bayes Formula, independence.
RANDOM VARIABLES AND EXPECTED VALUE: discrete and continuous random variables, mass distribution and density, distribution function, joint and marginal distributions, expected value and its properties, variance and covariance, weak law of large numbers.
EXAMPLES OF RANDOM VARIABLES: random variables of the following type: Bernoulli, binomial, Poisson, uniform, Gaussian, exponential, geometric.
INTRODUCTION TO STATISTICAL INFERENCE: the inference problem, parametric and non parametric inference
ELEMENTS OF PARAMETRIC ESTIMATES: random samples, estimators, mean squared error. Estimators for finite samples and their properties (bias and efficiency). Estimators for large samples (consistency and asymptotic normality). maximum likelihood method, estimates for intervals.
ELEMENTS OF HYPOTHESIS VERIFICATION: the statistical test, general facts, first order error, significance level and the p value. The power function of a test. Hypothesis test on the average of a Gaussian sample with given variance. Hypotesis test on the average of Gaussian sample with unknown variance.

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

Conoscere gli argomenti del programma ed essere in grado di risolvere esercizi

Prerequisites and Learning Activities

elementary mathematics and some notions of mathematical analysis

Assessment Methods and Criteria

written exam with exercises and theoric questions

Textbooks

S M Ross, Probabilità e statistica , Maggioli.

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 16 gennaio 2018, 14:08