International Students

#### Corsi di studio a esaurimento

Course partially running (all years except the first)

### Statistics

Course code
4S00121
Name of lecturer
Catia Scricciolo
Coordinator
Catia Scricciolo
Number of ECTS credits allocated
9
SECS-S/01 - STATISTICS
Language of instruction
Italian
Site
VERONA
Period
primo semestre (lauree) dal Sep 28, 2020 al Dec 23, 2020.

## Learning outcomes

The course aims at providing the basic techniques of descriptive statistics, probability and statistical inference to undergraduate students in economic and business sciences. Prerequisite to the course is the mastering of a few basic mathematical concepts such as limit, derivative and integration at the level of an undergraduate introductory course in calculus. Overall, these techniques provide the necessary toolkit for quantitative analysis in processes related to the observation and understanding of collective phenomena. From a practical point of view, they are necessary for descriptive, interpretative and decision-making purposes when carrying out statistical studies related to economic and social phenomena. In addition to providing the necessary mathematical apparatus, the course aims at providing conceptual tools for a critical evaluation of the methodologies considered.

## Syllabus

a) DESCRIPTIVE STATISTICS

• Data collection and classification; data types.

• Frequency distributions; histograms and charts.

• Measures of central tendency; arithmetic mean, geometric mean and harmonic mean; median; quartiles and percentiles.

• Variability and measures of dispersion; variance and standard deviation; coefficient of variation.

• Moments; indices of skewness and kurtosis.

• Multivariate distributions; scatterplots; covariance; variance of the sum of more variables.

• Multivariate frequency distributions; conditional distributions; chi-squared index of dependence; Simpson’s paradox.

• Method of least squares; least-squares regression line; Pearson’s coefficient of linear correlation; Cauchy-Schwarz inequality; R^2 coefficient; total, explained and residual deviance.

b) PROBABILITY

• Random experiments; sample space; random events and operations; combinatorics.

• Conditional probability; independence; Bayes' theorem.

• Discrete and continuous random variables; distribution function; expectation and variance; Markov and Tchebycheff's inequalities. Special discrete distributions: uniform, Bernoulli, Binomial, Poisson and geometric.
Special continuous distributions: continuous uniform, Gaussian, exponential.

• Multivariate discrete random variables; joint probability distribution; marginal and conditional probability distributions; independence; covariance; correlation coefficient.

• Linear combinations of random variables; average of independent random variables; sum of independent, Gaussian random variables.

• Weak law of large numbers; Bernoulli’s law of large numbers for relative frequencies; central limit theorem.

c) INFERENTIAL STATISTICS

• Sample statistics and sampling distributions; Chi-square distribution; Student's t distribution; Snedecor's F distribution.

• Point estimates and estimators; unbiasedness, efficiency, consistency; estimate of a mean, of a proportion, of a variance.

• Confidence intervals for a mean, for a proportion (large samples) and for a variance.

• Hypothesis testing; one and two tails tests for a mean, for a proportion (large samples) and for a variance; hypothesis testing for differences between two means, two proportions (large samples) and two variances.

Textbooks

- A. AZZALINI (2001) Inferenza statistica: una presentazione basata sul concetto di verosimiglianza, 2nd Ed.,
Springer Verlag Italia.
- E. BATTISTINI (2004) Probabilità e statistica: un approccio interattivo con Excel. McGraw-Hill, Milano.
- S. BERNSTEIN, R. BERNSTEIN (2003) Statistica descrittiva, Collana Schaum's, numero 109. McGraw-Hill, Milano.
- S. BERNSTEIN, R. BERNSTEIN (2003) Calcolo delle probabilita', Collana Schaum's, numero 110. McGraw-Hill, Milano.
- S. BERNSTEIN, R. BERNSTEIN (2003) Statistica inferenziale, Collana Schaum's, numero 111. McGraw-Hill, Milano.
- F. P. BORAZZO, P. PERCHINUNNO (2007) Analisi statistiche con Excel. Pearson, Education.
- D. GIULIANI, M. M. DICKSON (2015) Analisi statistica con Excel. Maggioli Editore.
- P. KLIBANOFF, A. SANDRONI, B. MODELLE, B. SARANITI (2010) Statistica per manager, 1st Ed., Egea.
- D. M. LEVINE, D. F. STEPHAN, K. A. SZABAT (2014) Statistics for Managers Using Microsoft Excel, 7th Ed.,
Global Edition. Pearson.
- M. R. MIDDLETON (2004) Analisi statistica con Excel. Apogeo.
- D. PICCOLO (1998) Statistica, 2nd Ed. 2000. Il Mulino, Bologna.
- D. PICCOLO (2010) Statistica per le decisioni, New Ed. Il Mulino, Bologna.

Teaching methods

Course load is equal to 84 hours: the course consists of 48 lecture hours (equal to 6 ECTS credits) and of 36 exercise hours (equal to 3 ECTS credits).

Study Guide

A detailed syllabus will be made available at the end of the course on the e-learning platform.

Prerequisites

Students are supposed to have acquired math knowledge of basic concepts like limit, derivative and integral.

Exercise sessions

Exercise sessions are integral part of the course and are necessary to adequate understanding of the topics.

Tutoring activities

There will be optional tutoring hours devoted to exercises before each exam session. More detailed information will be made available in due course.

 Reference books Author Title Publisher Year ISBN Note W. Feller An Introduction to Probability Theory and Its Applications, Volume 1 (Edizione 3) Wiley 1968 P. Baldi Calcolo delle Probabilità (Edizione 2) McGraw-Hill 2011 9788838666957 S. Lipschutz Calcolo delle Probabilità, Collana Schaum ETAS Libri 1975 P. Baldi Calcolo delle Probabilità e Statistica (Edizione 2) Mc Graw-Hill 1998 8838607370 T. Mikosch Elementary Stochastic Calculus With Finance in View World Scientific, Singapore 1999 R. V. Hogg, A. T. Craig Introduction to Mathematical Statistics (Edizione 5) Macmillan 1994 D. M. Cifarelli Introduzione al Calcolo delle Probabilità McGraw-Hill, Milano 1998 A. M. Mood, F. A. Graybill, D. C. Boes Introduzione alla Statistica McGraw-Hill, Milano 1991 G. R. Grimmett, D. R. Stirzaker One Thousand Exercises in Probability Oxford University Press 2001 0198572212 A. N. Shiryaev Probability (Edizione 2) Springer, New York 1996 G. R. Grimmett, D. R. Stirzaker Probability and Random Processes (Edizione 3) Oxford University Press 2001 0198572220 G. R. Grimmett, D. R. Stirzaker Probability and Random Processes: Solved Problems (Edizione 2) The Clarendon Press, Oxford University Press, New York 1991 J. Jacod, P. Protter Probability Essentials Springer, New York 2000 G. Casella, R. L. Berger Statistical Inference (Edizione 2) Duxbury Thompson Learning 2002 G. Cicchitelli, P. D'Urso, M. Minozzo Statistica: principi e metodi (Edizione 3) Pearson Italia, Milano 2018 9788891902788 S. E. Shreve Stochastic Calculus for Finance II: Continuous-Time Models Springer, New York 2004 S. E. Shreve Stochastic Calculus for Finance I: The Binomial Asset Pricing Model Springer, New York 2004 B. V. Gnedenko Teoria della Probabilità Editori Riuniti Roma 1979

## Assessment methods and criteria

Teaching methods and assessment of learning will be illustrated as soon as there will be more information about the context rules necessary to resolve the provision of teaching in the next academic year.

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