PROBABILITY AND STATISTICS

The course is one of the quantitative training activities of the Bachelor degree in Digital Management. The aim is to get the student familiar with the main statistical tools for use in management, economics and finance, under conditions of uncertainty.
The course provides knowledge of descriptive statistics, probability and inference, as well as skills in the use of specific programs for analysing data and reporting.
At the end of the course, the student will be able to identify suitable models and methodologies in the context of interest; moreover he will learn to interpret and communicate the obtained results, with the aim of driving appropriate decisions.

1. Knowledge and understanding:
- to know the main tools for graphical representation and summary of a dataset
- to know the basic concepts of probability calculus and distributions for inference
- to know the basic methodologies of statistical inference

2. Ability to apply knowledge and understanding:
- to use specific programs for data analysis and reporting
- to use the appropriate terminology in all the processes of application and communication of the acquired knowledge

3. Ability to judge:
- to apply the acquired knowledge in a specific context, identifying the most appropriate models and methods

4. Communication skills:
- to present in a clear and exhaustive way the results obtained from a statistical analysis
- to know how to interact with the other students and with the instructor during the classes and on the virtual forum

5. Learning skills:
- to use and integrate information from notes, books, slides, videos and practical lab sessions
- to assess the achieved knowledge through quizzes, exercises and assignments during the course

Mathematics for decision sciences (both modules) is propaedeutic.

The course provides a practical introduction to probability and statistics. The aim of the first part of the course is to get the students familiar with the most useful statistical techniques for summarising and representing datasets. Then some basic concepts about elementary probability and distributions are presented. The last part is devoted to statistical inference methods for estimation, testing and prediction. Theoretical presentations are always motivated by practical examples and applications to economic and business problems. The use of the statistical package R (http://cran.r-project.org/ ) is also introduced for data analysis and inference.

Descriptive statistics: population and samples; types of variables; basic graphical representations and summaries for numerical variables and factors; relationship between two factors and the Chi-squared statistics; relationship between two numerical variables, correlation and regression.
Probability: sample space, events and probability; independence; discrete and continuous random variables; the binomial and the normal distributions.
Inference: sample distributions; estimation of the mean and the standard deviation of a population; confidence intervals; hypotheses testing and p-values.

Robinson, R. and White, H. (2016) Elementary Statistics with R. Available at http://homerhanumat.github.io/elemStats/

The achievement of the course objectives is assessed through participation in activities during the course (20%) and a written final exam (80%). The use of the software R is part of the program of the course and the main tool for solving the assignments and for the exam.
Among the activities proposed during the classes there will be quizzes to assess understanding of basic concepts and group works. Active participation in these activities is evaluated 7 points maximum.
The final exam (26 points) is a Moodle quiz composed by exercises similar to those solved or assigned during the course. The quiz is an open book exam, so that it is possible to use all the material in Moodle and R for the calculations. An example of exam will be made available in Moodle.
Students with a grade in the written exam equal or higher than 22, may ask to improve their final grade with an oral exam. The oral exam substitutes the activities during the course, it is about the whole program of the course and may increase or decrease the grade in the written exam.

written

1. Scores in the range of 18-22 will be assigned when:
- adequate ability to use specific knowledge for data analysis
- sufficient ability to apply the acquired knowledge in a specific context, identifying the most appropriate probabilistic models and methods
- limited ability to critically interpret the obtained results
- sufficient communication skills, using rigorous formulas and appropriate terminology
2. Scores in the range of 22-26 will be assigned when:
- good ability to use specific knowledge for data analysis
- adequate ability to apply the acquired knowledge in a specific context, identifying the most appropriate probabilistic models and methods
- sufficient ability to critically interpret the obtained results
- adequate communication skills, using rigorous formulas and appropriate terminology
3. Scores in the range of 26-30 will be assigned when:
- excellent ability to use specific knowledge for data analysis
- good or excellent ability to apply the acquired knowledge in a specific context, identifying the most appropriate probabilistic models and methods
- good ability to critically interpret the obtained results
- good or excellent communication skills, using rigorous formulas and appropriate terminology
4. Honors will be granted to students in the range 3. that have participated with commitment and interest to the activities during the course or that have shown excellent mastery of the subject.

Interactive approach based on classic lectures, cooperative activities and practical lab sessions. Use of e-learning platforms for discussions and learning assessment. Open-source programs for data analysis and reporting.

English