TEORIA DEI SEGNALI A - LModule ELEMENTI DI PROBABILITA' E STATISTICA PER L'ICT
Academic Year 2025/2026 - Teacher: CHRISTIAN GRASSOExpected Learning Outcomes
The course aims to provide students with the basic notions of statistics and probability theory. In relation to Dublin Descriptor 1 (Knowledge and understanding) and Descriptor 2 (Applying knowledge and understanding), the course is intended to give students a general understanding of simple problems described using statistical and probabilistic methods. By combining these tools with those acquired in Module B of the same course, students will be able to understand the concept of a random process and its characteristics, and will then apply the acquired knowledge to the solution of real engineering problems.
In relation to Dublin Descriptors 3 (Making judgments), 4 (Communication skills), and 5 (Learning skills), the goal of the course module is for students to acquire the ability to understand the principles underlying statistics and probability, making the concept of randomness of an experiment and the definition of random variable their own. Students will be able to further explore what they have learned during the course and use their basic knowledge as a starting point for the following module and for future subjects.
Furthermore, upon passing the exam, students will acquire the ability to mathematically formalize the results of transformations of random variables and to represent (both graphically and through characteristic indices) data samples and populations, with the capacity to communicate their acquired knowledge to others in a clear and complete way. Finally, students will understand and be able to formalize the transformations carried out by the basic components of a communication system, applying the above knowledge to the solution of real problems.
Students will thus become independent from the teacher, gaining the ability to refine and deepen their knowledge autonomously and creatively. By the end of the course, students will have developed the ability to carry out autonomous and critical investigation, as well as to formalize real problems using statistical methods (also through the many exercises carried out during the course), and the ability to discuss and present the results of such studies. Lastly, with the tools acquired during the course, students will be able to continue independently with the study of other engineering subjects, also mastering statistical investigation tools.
Course Structure
The course, divided into two modules—one on “Elements of Probability and Statistics for ICT” (held during the first semester) and the other on “Deterministic and Random Signals” (held during the second semester)—is organized into lectures and exercises, both on the board and on the computer. In case of a COVID emergency, the lectures and exercises may be held on a designated online platform indicated by the university. If the course is delivered in a hybrid or remote mode, necessary changes may be introduced to the previously stated format to ensure the scheduled program, as outlined in the syllabus, is followed. The lectures are highly interactive, with contributions from both the instructor and students, who are invited to carry out exercises with the support of the instructor.
Finally, a series of seminars is usually scheduled at the end of the course, demonstrating the application of signal theory and spectral analysis to signal modulation and filtering using laboratory equipment (oscilloscope, filters, modulators/demodulators).
Required Prerequisites
Attendance of Lessons
Detailed Course Content
Data collection and descriptive statistics, statistical inference and probabilistic models, *populations and samples.
*Data organization (frequency tables and charts, relative frequency tables and charts, histograms, ogives, stem and leaf plots), *measures that summarize data (mean, median, sample mode, variance, standard deviation, sample percentiles, and box plots), *Chebyshev's inequality, *normal samples, *bivariate data sets.
*Random experiment; probability, *Bayes' theorem; *total probability theorem; *random variables; *probability density function and cumulative distribution of notable random variables; *transformation of a random variable; *characteristic indices of a distribution; *Gaussian random variable; *other notable random variables; pairs of random variables; *central limit theorem.
*Maximum likelihood estimators, *confidence intervals, *estimates for the difference between the means of two normal populations, *Bayesian estimators.
Textbook Information
1) Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill
2) Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Data collection and descriptive statistics, statistical inference and probabilistic models, populations and samples (4 hours theory + 6 hours exercises) | Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo - chapter 1 |
| 2 | Data organization (frequency tables and charts, relative frequency tables and charts, histograms, ogives, stem and leaf plots), measures that summarize data (mean, median, sample mode, variance, standard deviation, sample percentiles, and box plots), Chebyshev's inequality, normal samples, bivariate data sets (4 hours theory + 6 hours exercises) | Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo - chapter 2 |
| 3 | Probability, Bayes' and total probability theorems; random variables, PDF and CDF functions, and moments; random variable (RV) transformation; pairs of RVs; Gaussian random variable; central limit theorem (16 hours theory + 12 hours exercises) | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill - chapter 8 |
| 4 | Maximum likelihood estimators, confidence intervals, estimates for the difference between the means of two normal populations, Bayesian estimators, examples (4 hours theory + 6 hours exercises) | Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo - chapter 7 |
Learning Assessment
Learning Assessment Procedures
Unless there is a COVID emergency, a midterm written exam takes place to assess the ability to solve problems described in statistical and probabilistic terms. The midterm exam takes place at the end of the first semester and lasts two hours. It consists of two exercises and two open-ended theoretical questions. If passed, the midterm exempts the student from the portion of the final exam related to Module 1 on Elements of Probability and Statistics for ICT. The grade obtained in the midterm contributes half of the final evaluation.
Unless there is a COVID emergency, the final exam is written and lasts two hours. It consists of two exercises and two open-ended theoretical questions. If the student has passed the midterm, the exercise and theoretical question concerning Module 1 will be replaced by an exercise and a question focused on Module 2.
Each exercise and each theoretical question is worth up to 10 points. The total score will be multiplied by 3 and divided by 4.
To pass any exam, it is necessary to obtain at least 10 points in the two exercises.
The theoretical questions may include the discussion of theorems. The proof of the theorems contributes to the grade, but it is not required to pass the exam.
Students who obtain a grade of 18 or higher on the written exam may take an oral exam. Depending on the outcome of the oral exam, the grade may increase or decrease by up to three points.
Finally, students who wish to do so may prepare and discuss up to three short papers, each of which can contribute one point to the final grade.