Training and Research
PhD Programme Courses/classes - 2019/2020
Lezioni Dottorandi
Credits: 50
Language: Italian
Teacher: Valeria Franceschi, Catia Scricciolo
Behavioral and Experimental Economics
Credits: 5
Language: Italian
Teacher: Maria Vittoria Levati, Chiara Nardi, Luca Zarri
Corporate governance
Credits: 4
Language: Italian
Teacher: Alessandro Lai
Development Economics
Credits: 4
Language: Italian
Teacher: Federico Perali
Econometrics for management
Credits: 4
Language: Italian
Teacher: Francesca Rossi, Laura Magazzini
Energy Economics
Credits: 2,5
Language: Italian
Teacher: Luigi Grossi
Game Theory
Credits: 4
Language: Italian
Teacher: Francesco De Sinopoli
Inequality
Credits: 5
Language: Italian
Teacher: Francesco Andreoli, Claudio Zoli
Macro economics
Credits: 2,5
Language: Italian
Teacher: Alessia Campolmi
Macroeconomics I
Credits: 10
Language: Italian
Teacher: Claudio Zoli, Angelo Zago, Martina Menon
Mathematics
Credits: 7,5
Language: Italian
Teacher: Alberto Peretti, Athena Picarelli, Letizia Pellegrini
Organization Theory
Credits: 4
Language: Italian
Teacher: Cecilia Rossignoli, Alessandro Zardini, Lapo Mola
Political economy
Credits: 5
Language: Italian
Teacher: Emanuele Bracco, Roberto Ricciuti, Marcella Veronesi
Probability
Credits: 7,5
Language: Italian
Teacher: Marco Minozzo
Metodi quantitativi per la gestione aziendale
Credits: 5
Language: Italian
Teacher: Riccardo Scarpa
Statistica
Credits: 7,5
Language: Italian
Supply Chain Management
Credits: 4
Language: Italian
Teacher: Barbara Gaudenzi
Probability (2019/2020)
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 - 2019/2020
PhD School training offer to be defined
Faculty
Magazzini Laura
laura.magazzini@univr.it 045 8028525Manzoni Elena
elena.manzoni@univr.it 8783PhD students
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