STATISTICS - 2

This course is part of the “core educational activities” of the bachelor degree program. It is a single 12 credit compulsory course taught in two terms (one semester). The course aims at introducing the statistical inference principles and tools most commonly used in economic empirical analysis. Estimation and hypothesis testing are illustrated for both the main parametric models and some relevant nonparametric applications (goodness of fit, independence, homogeneity). A relevant part of the course concerns those probability theory topics that are propedeutical to inferential techniques.

The course aims at providing an adequate knowledge of the main probabilistic and inferential tools used in the empirically based analysis and interpretation of economic phenomena.

The exam of Mathematics (ET0045) is a prerequisite for the exam of Statistics. Therefore, the topics covered by both Matematics (ET0045) and Mathematics: prerequisites (ET0101) courses are assumed to be known.

The program of the 12 credit course is the following:

1. Elementary probability calculus: definitions, axioms and property of the probability measure; conditional probability and stochastic independence; Bayes theorem.
2. Random variables: discrete and continuous variables; expected value and moments; quantiles; transformations of random variables; some relevant models of univariate random variables; bivariate discrete random variables, covariance and correlation; some relevant properties of multivariate random variables; sequencies of random variables, laws of large numbers, the central limit theorem.
3. Descriptive statistics: data collection and classification; frequency distributions; the main statistica indeces; graphical tools.
4. Statistical inference: parametric statistical model and sampling; point and interval estimation; hypothesis testing; goodness of fit, independence and homogeneity testing.

Textbook:
Boella M., Probabilità e Statistica per ingegneria e scienze. Pearson - Prentice Hall. II ed. 2020. Chapter 1 (section 1.8 can be omitted); Chapter 2 (sections 2.5.3 , 2.6.2, 2.6.6. and 2.8 can be omitted); Chapter. 3 (sections 3.1.3, 3.1.4, 3.5 can be omitted); Chapter 4 (sections 4.4, 4.6, 4.7.2 and 4.8 can be omitted); Chapter. 5 (section 5.3.3 can be omitted); Chapter 6 (sections 6.2, 6.3.3 and 6.4.2 can be omitted); Chapter 7 (sections 7.3.3, 7.4.4, 7.4.5 and 7.4.6 can be omitted); Appendix A, Appendix B (section B.4.2 can be omitted), Appendix C, Appendix D (sections from D.6 to D.13 can be omitted)

Further readings (exercises and applications):
Grigoletto M., Ventura L., Statistica per le Scienze Economiche: Esercizi con Richiami di Teoria, Giappichelli, 1998
Pauli F., Trevisani M., Torelli N., Statistica: esercizi ed esempi, Pearson, 2008

The final assessment consists of a written test and an oral interview at the teacher's discretion. Examples of questions are available on the Ca' Foscari Moodle e-learning platform. Regarding the grading, the exam will be marked on a scale ranging from 0 to 30. The minimum passing grade is 18. Honors ("lode") will be granted only for exceptional capacity of judgment and excellent knowledge of the topics under evaluation.

The course is taught through presentation style lectures and classroom practicals integrated by the individual student activities. Students are supported by the indicated textbook and by the resources made available on Moodle platform.

written and oral