PROBABILITY AND STATISTICS-2

This course belongs to the interdisciplinary educational activities of the Data Science curriculum of the Bachelor in Computer Science. The course aims at providing students with the basic tools of statistical inference and data analysis. The objective of the course is to develop skills to answer statistical questions that arise in the technological, scientific, biomedical, economic and business fields. Special attention will be paid to the integration of the methodology with computational tools through the use of the R language. The achievement of the educational objectives of the course allows the student to obtain the basis for learning more advanced data science tools.

Regular and active participation in the teaching activities and individual study will allow students to:
1. Knowledge and understanding capacity:
-- know and understand the main inferential methods
2. Ability to apply knowledge and understanding:
-- synthetize and model phenomena characterized by variability and uncertainty
-- use statistical software for data manipulation, synthesis and analysis
3. Independence of judgment:
-- correctly interpret the results of analyses produced by statistical softwares
4. Communication skills:
-- to present in a clear and exhaustive way the results obtained from a statistical data analysis, using rigorous formulas and appropriate terminology
5. Learning skills:
-- to use and merge information from notes, books, slides and practical sessions
-- to assess the achieved knowledge through quizzes, exercises and assignments during the course

It is assumed that the student has achieved the educational objectives of the Probability and Statistics - 1 course. It is important that students have a solid familiarity with the main properties and operations involving discrete and continuous random variables.

The course program includes presentation and discussion of the following topics:

1. Basic concepts
2. Point estimation
3. Interval estimation
4. Hypothesis testing
5. Dependence
Methods will be illustrated with simulated and real data using the R language (www.r-project.org).
The use of the software R is part of the programme of the course and the main tool for solving the assignments.

Main textbooks:
- Baron M (2014). Probability and Statistics for Computer Scientistis. Second Edition. CRC Press. Selected parts of chapters 8-9-10-11
- Mor Harchol-Balter (2024). Introduction to probability for Computing. Cambridge University Press. (Disponibile online: https://www.cs.cmu.edu/~harchol/Probability/book.html )
- Further readings and materials distributed during the course through the Moodle platform

Other suggested books:
S.M. Ross (2004). Calcolo delle probabilità. Apogeo.
M. Boella (2011). Probabilità e statistica per ingegneria e scienze. Pearson Italia, Milano.
G. Espa, R. Micciolo (2014). Problemi ed esperimenti di statistica con R. Apogeo.
H. Hsu (2011). Probabilità, variabili casuali e processi stocastici. McGraw-Hill.
R.A. Johnson (2007). Probabilità e statistica per ingegneria e scienze. Prentice Hall.
W. Navidi (2006). Probabilità e statistica per l'ingegneria e le scienze. McGraw-Hill.
S.M. Ross (2003). Probabilità e statistica per l'ingegneria e le scienze. Apogeo.

Course Evaluation Method:
The assessment for the entire course (12 CFU) is a written exam consisting of two partial exams. Each partial exam is worth a maximum of 31 points and lasts 90 minutes.
To pass the course, students must achieve a sufficient score in each of the two partial exams, meaning at least 18 points in each.
- Sequential Requirement: Only students who have passed the first partial exam are eligible to take the second.
- Full Exam Option: It is possible to take the complete exam by performing both partials on the same day, but strictly in succession. If the score for the first partial is insufficient, the second partial will not be graded.
- Validity: Both partial exams must be passed within the same academic year. Once the first partial is passed, the score remains valid for the remaining exam sessions of that academic year only, until the second partial is passed.
- Final Grade: Once both partial exams are passed, the final grade will be the average of the two scores. An overall score exceeding 30 points corresponds to a grade of cum laude (lode).

Instructions for the Second Partial Exam (6 CFU):
The first partial exam will cover the material of Module 1 only. The use of R is an important part of the course and will be subject to evaluation through the adequate use of commands in the written exam.
The exam will be composed of the following:
- One open question on theory (5 points): Evaluation will focus on the clarity, completeness, correctness, and conciseness of the response.
- Six single-choice questions (1 point each): Only the final answer will be marked; no justification or procedure trace is required.
- Three exercises (7 points each): A justification is required and carries a higher value than the final numerical answer. Clarity and order will also be taken into consideration during grading.
Exam Rules:
+ Closed book exam: However, a formulary is allowed. Each student is responsible for their own formulary, which must be completely contained on both sides of one A4 sheet.
+ An adequate calculator is required. It is the student's responsibility to bring a functioning calculator and to know how to use it.

written

Regarding the grading scale, exam grades will depend on the level of the capabilities shown:
- Sufficient (18-22 points): to students who demonstrate a sufficient theoretical knowledge base and capacity to apply the concepts covered throughout the course, as well as a sufficient capacity to elaborate and present results using the specific language and mathematical notation associated to probability models and their interpretation
- Good (23-26 points): to students who demonstrate a good theoretical knowledge base and capacity to apply the concepts covered throughout the course, as well as a good capacity to elaborate and present results using the specific language and mathematical notation associated to probability models and their interpretation
- Very good (23-26 points): to students who demonstrate a very good superior theoretical knowledge base and capacity to apply the concepts covered throughout the course, as well as a very good or superior capacity to elaborate and present results using the specific language and mathematical notation associated to probability models and their interpretation and at least a basic capacity to identify relations between different concepts covered throughout the course and formulate independent judgement.
- Honors will be granted to students exhibiting an excellent knowledge base anc capacity to apply the concepts covered during the course through the use of specific language and mathematical notation, including the identification of relationships between different concepts and definitions.

Theoretical lectures and exercises at the blackboard and with PC using R. Use of the Moodle platform for learning assessment during the course.