
Course unit
PROBABILITY AND STATISTICS
SC03106737, A.A. 2016/17
Information concerning the students who enrolled in A.Y. 2015/16
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/06 
Probability and Mathematical Statistics 
6.0 
Course unit organization
Period 
Second semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
16 
34.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
3 a.a 2018/2019 
01/10/2018 
28/02/2020 
COLLET
FRANCESCA
(Presidente)
FONTANA
CLAUDIO
(Membro Effettivo)
BARBATO
DAVID
(Supplente)
FISCHER
MARKUS
(Supplente)
VARGIOLU
TIZIANO
(Supplente)

2 a.a 2017/2018 
01/10/2017 
28/02/2019 
FORMENTIN
MARCO
(Presidente)
BARBATO
DAVID
(Membro Effettivo)
BIANCHI
ALESSANDRA
(Membro Effettivo)
FERRANTE
MARCO
(Membro Effettivo)
FISCHER
MARKUS
(Membro Effettivo)
VARGIOLU
TIZIANO
(Membro Effettivo)

Prerequisites:

Familiarity with the basic notions of analysis, linear algebra and combinatorics. The courses "Analisi matematica" and "Algebra e matematica discreta" cover all the necessary prerequisites. 
Target skills and knowledge:

The student will acquire a basic knowledge of probability theory and inferential statistics. Those that will pass the exam will be able to build simple probabilistic models of uncertain phenomena and carry out the necessary probabilistic and/or statistical computations. 
Examination methods:

3 hour written test, closed book. 
Assessment criteria:

The student will have to master the theoretical concepts and show his ability to apply them to solve problems of probability and statistics of appropriate difficulty. 
Course unit contents:

Probability theory. Axioms and their elementary consequences. Examples of discrete, finite, and uniform probability spaces. The birthday problem. Conditional probability. Law of total probability, Bayes formula. Independent events. Random variables and vectors. Joint discrete distributions and densities. Independent random variables. Moments: expectation, variance, higher moments, correlation, covariance. Inequalities: Jensen, Markov, Chebishev. Examples of discrete random variables: Bernoulli, binomial, geometric, Poisson. Poisson limit theorem. Absolutely continuous random variables, uniform, exponential, normal. Weak law of large numbers (Chebyshev). The method of Montecarlo. Central limit theorem (Lindeberg Lévy). Normal approximation.
Descriptive statistics. Qualitative and quantitative data, relative frequencies, graphical methods. Empirical indices: location, centrality, dispersion, shape. Correlation between variables: regression line, correlation, correlation coefficient.
Inferential statistics. Estimators. Confidence intervals. Statistical tests: hypothesis and alternative, critical region, critical value, type I and type II errors, power, pvalue, bilateral and unilateral tests. Tests for the mean and for difference of means. Paired tests. Tests for proportions: contingency tables and chisquare tests. 
Planned learning activities and teaching methods:

Traditional lectures. A typical lecture consists of theoretical developments, examples and counterexamples, and exercises. Through the moodle platform graded solved exercises are assigned at the end of each lecture. 
Additional notes about suggested reading:

The lectures cover all the topics on which the exam is based. The moodle platform contains several teaching aids: a set of notes on probability theory, several sheets of graded exercises and their solutions. 
Textbooks (and optional supplementary readings) 

M. Bramanti, Calcolo delle probabilità e statistica. Bologna: Progetto Leonardo, .

Lorenzo Finesso, Appunti di Probabilità. : , . Available on Moodle


