Training and Research
PhD Programme Courses/classes - 2020/2021
Academic writing in latex and academic presentation
Credits: 2,5
Language: Italian
Advanced English for Academic Skills
Credits: 2,5
Language: Italian
Agenda dell’organizzazione delle nazioni unite 2030 sullo sviluppo sostenibile, ricerca e diritto antidiscriminatorio: strumenti ed esperienze nelle università
Credits: 1
Language: Italian
Artificial intelligence, cybersecurity e diritto
Credits: 1
Language: Italian
Behavioral and Experimental Economics
Credits: 5
Language: Italian
Teacher: Luca Zarri, Simone Quercia, Maria Vittoria Levati
Comunicare la scienza: il ruolo dei ricercatori e il rapporto tra esperti, cittadini e istituzioni
Credits: 0,5
Language: Italian
Corporate Governance
Credits: 5
Language: Italian
Teacher: Alessandro Lai
Corso di inglese B1/certificazione B1
Credits: 2,5
Language: Italian
Corso di inglese B2/certificazione B2
Credits: 2,5
Language: Italian
Corso di inglese C1/certificazione C1
Credits: 2,5
Language: Italian
Corso di lingua italiana per stranieri
Credits: 2,5
Language: Italian
Corso di programmazione con matlab
Credits: 2
Language: Italian
Medical statistics with R
Credits: 3
Language: Italian
Basic statistics course
Credits: 2,5
Language: Italian
Intermediate statistics course
Credits: 2,5
Language: Italian
(Meta-analysis using the statistical software Stata and R
Credits: 1,5
Language: Italian
Corso teorico-pratico di microscopia di base
Credits: 1
Language: Italian
Development economics
Credits: 5
Language: Italian
Teacher: Federico Perali
Diritto d'autore e brevetti
Credits: 1
Language: Italian
Dissemination dei risultati della ricerca
Credits: 1
Language: Italian
Econometrics for management
Credits: 7,5
Language: Italian
Teacher: Diego Lubian, Francesca Rossi, Alessandro Bucciol
Economia dei Mercati Energetici
Credits: 5
Language: Italian
Teacher: Luigi Grossi
English for academic presentations
Credits: 2,5
Language: Italian
English for academic writing
Credits: 2,5
Language: Italian
Finanza
Credits: 5
Language: Italian
Teacher: Cecilia Mancini
Game Theory
Credits: 5
Language: Italian
Teacher: Francesco De Sinopoli
Inequality
Credits: 5
Language: Italian
Teacher: Francesco Andreoli, Claudio Zoli
Introduzione al “public speaking”
Credits: 1
Language: Italian
La mia archeologia e la mia politica culturale
Credits: 0,5
Language: Italian
Python programming language
Credits: 2,5
Language: Italian
Macro economics
Credits: 5
Language: Italian
Teacher: Michele Imbruno, Alessia Campolmi
Mathematics
Credits: 7,5
Language: Italian
Teacher: Letizia Pellegrini, Alberto Peretti
Microeconomics 1
Credits: 10,5
Language: Italian
Teacher: Tamara Fioroni, Claudio Zoli, Martina Menon
Organization Theory
Credits: 5
Language: Italian
Teacher: Cecilia Rossignoli
Political economy
Credits: 5
Language: Italian
Teacher: Emanuele Bracco, Roberto Ricciuti, Marcella Veronesi
Presentation of Horizon Europe framework programme
Credits: 1
Language: English
Probability
Credits: 7,5
Language: Italian
Teacher: Marco Minozzo
Project writing for beginners
Credits: 1
Language: Italian
Qualitative methodologies in management studies
Credits: 5
Language: Italian
Teacher: Cecilia Rossignoli, Riccardo Stacchezzini
Quantitative methodologies in management studies
Credits: 5
Language: Italian
Teacher: Riccardo Scarpa, Diego Begalli
Seminario Consigliera di fiducia
Credits: 1
Language: Italian
Software R
Credits: 2,5
Language: Italian
Teacher: Flavio Santi
Spin off e start-up innovative
Credits: 1
Language: Italian
Statistica
Credits: 7,5
Language: Italian
Teacher: Catia Scricciolo
Supply Chain Management
Credits: 5
Language: Italian
Teacher: Barbara Gaudenzi
Protecting psychological well-being in the PhD program: development and enhancement of personal strategies and attitudes that predispose to professional satisfaction and ethical collaboration.
Credits: 1
Language: Italian
Probability (2020/2021)
Teacher
Referent
Credits
7.5
Language
Italian
Class attendance
Free Choice
Location
VERONA
Learning outcomes
Availability
The course is intended for 1st year students on PhD in Economics and Management.
Pre-requisites
Introduction to mathematics, elementary statistical theory and elementary set theory. Basic knowledge of probability theory, as in: P. Newbold, W. Carlson, B. Thorne (2012), Statistics for Business and Economics, Pearson Higher Education, Chapters 3-5 (previous editions would be fine as well). Attendance at more advanced courses such as real analysis, probability, distribution theory and statistical inference would be desirable.
Objectives of the course
The purposes of this course are: (i) to explain, at an intermediate level, the basis of probability theory and some of its more relevant theoretical features; (ii) to explore those aspects of the theory most used in advanced analytical models in economics and finance. The topics will be illustrated and explained through many examples.
Program
Course content
1. Algebras and sigma-algebras, axiomatic definition of probability, probability spaces, properties of probability, conditional probability, Bayes theorem, stochastic independence for events.
2. Random variables, measurability, cumulative distribution functions and density functions.
3. Transformations of random variables, probability integral transform.
4. Lebesgue integral, expectation and variance of random variables, Markov inequality, Tchebycheff inequality, Jensen inequality, moments and moment generating function.
5. Multidimensional random variables, joint distributions, marginal and conditional distributions, stochastic independence for random variables, covariance and correlation, Cauchy-Schwartz inequality.
6. Bivariate normal distribution, moments, marginal and conditional densities.
7. Transformations of multidimensional random variables.
8. Convergence of sequences of random variables, weak law of large numbers and central limit theorem.
Textbook
S. Ross (2010). A First Course in Probability, 8th Edition. Pearson Prentice Hall.
Further readings
G. Casella, R. L. Berger (2002). Statistical Inference, Second edition. Duxbury Thompson Learning.
R. Durrett (2009). Elementary Probability for Applications. Cambridge University Press.
M. J. Evans, J. S. Rosenthal (2003). Probability and Statistics - The Science of Uncertainty. W. H. Freeman and Co.
G. Grimmett, D. Stirzaker (2001). Probability and Random Processes. Oxford University Press.
A. M. Mood, F. A. Graybill, D. C. Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
P. Newbold, W. Carlson, B. Thorne (2012). Statistics for Business and Economics. Pearson Higher Education.
D. Stirzaker (2003). Elementary Probability. Cambridge University Press.
L. Wasserman (2004). All of Statistics. Springer.
Advanced readings
R. B. Ash, C. A. Doléans-Dade (2000). Probability and Measure Theory. Harcourt/Academic Press.
M. J. Schervish (1995). Theory of Statistics. Springer.
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| S. Ross | A First Course in Probability (Edizione 8) | Pearson Prentice Hall | 2010 | ||
| L. Wasserman | All of Statistics | Springer | 2004 | ||
| D. Stirzaker | Elementary Probability | Cambridge University Press | 2003 | ||
| R. Durrett | Elementary Probability for Applications | Cambridge University Press | 2009 | ||
| A. M. Mood, F. A. Graybill, D. C. Boes | Introduction to the Theory of Statistics | McGraw-Hill | 1974 | ||
| R. B. Ash, C. A. Doléans-Dade | Probability and Measure Theory | Harcourt/Academic Press | 2000 | ||
| G. R. Grimmett, D. R. Stirzaker | Probability and Random Processes (Edizione 3) | Oxford University Press | 2001 | 0198572220 | |
| M. J. Evans, J. S. Rosenthal | Probability and Statistics - The Science of Uncertainty | W. H. Freeman and Co. | 2003 | ||
| G. Casella, R. L. Berger | Statistical Inference (Edizione 2) | Duxbury Thompson Learning | 2002 | ||
| P. Newbold, W. Carlson, B. Thorne | Statistics for Business and Economics | Pearson Higher Education | 2012 | ||
| M. J. Schervish | Theory of Statistics | Springer | 1995 |
Examination Methods
A two-hour written paper at the end of the course.
PhD school courses/classes - 2020/2021
PhD School training offer to be defined
Faculty
silvia.cavalieri@univr.it
michele.imbruno@univr.it
Manzoni Elena
elena.manzoni@univr.it
8783
0458028706
Nicodemo Catia
catia.nicodemo@univr.it
+39 045 8028340
0458028706
dora.renna@univr.it
Santi Flavio
flavio.santi@univr.it
045 802 8239
riccardo.scarpa@univr.it
marcella.veronesi@univr.it
PhD students
amiem.jobe@univr.it
enockdesmond.opoku@univr.it
andrea.xamo@univr.it
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