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):
Monti, A. C.: Statistica. Esercizi svolti. Pearson, 2024, capitoli 1-26.

The final assessment consists of a written test of multiple-choice questions, and an oral test. There are no intermediate assessments or differentiated assessments for attending or non-attending students.
The written test is intended to test calculating ability and understanding of the fundamental concepts of the discipline. During the written test, the use of books, notes, electronic media, with the exception of a calculator and statistical tables, is not allowed. There is a penalty in the score for multiple choice questions with incorrect answers.
The oral test is entered having obtained a sufficient result in the written test. The oral test, on the other hand, is intended to test argumentative skills and the correct use of statistical-probabilistic language. During the oral test, therefore, the student must demonstrate knowledge of the topics covered in the course and the ability to expound them in a formal manner.
Examples of multiple-choice questions and questions asked in the oral exam are available in the area dedicated to the course in the University's Moodle e-learning platform.

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