PROBABILITY AND RANDOM
This course is designed to motivate the students for use of probabilistic models in engineering analysis and design, to equip the students with the basics of probability theory and to introduce commonly used probabilistic models and their applications.
Knowledge and understanding:fundamentals of the theory of probability, models of RVs and their transformation, random processes (continuous and discrete time) and their energetic characterisation, acf.
Applying knowledge and understanding: the student must be able to analyse random phenomena, to apply the fundamentals of the theory of probability to solve simple problems, to manage random vectors and signals, to calculate the PSD and ESD.
Making judgements: the student must be able to identify the main techniques to analyse a random phenomenon.
Communication skills: the student must be able to explain the subjects of the course, by using the precise scientific language.
Learning skills: the student must be able to consult books and papers different from those adopted by the teacher.
Mathematics, Fundamentals of Algebra and Geometry, and Signal Theory.
Probability (9h lessons+3h exercises): Sets, events, and probability. Random variables (19h lessons+10h exercises+ 3h Matlab): Random variables, discrete and continuous distributions. Distributions of functions of a random variable. Expected values and moments. Common families of distributions. Multiple random variables (7h lessons+4h exercises + 2h Matlab): Joint and marginal distributions. Conditional distributions and independence. Covariance and correlation. First elements of information theory. Random processes (10h lessons+5h exercises): Random processes. Expectation and acf. Bernoulli process. Stationarity. Cyclostationarity. ESD. PSD. PAM signal. Relationship between acf at the input and output of LTI systems. Theorem of Wiener-Kinchine. Gaussian processes.
Probability. Random variables. Random vectors. Random processes. Elements of Information theory.
Lectures. Exercises. Matlab laboratory.
 Giacinto Gelli - Probabilità e informazione (fifth version, September 2003).  Athanasios Papoulis - Probability, Random Variables, and Stochastic Processes, ed. McGraw-Hill, third edition.  Alberto Leon-Garcia, "Probability and Random Processes for Electrical Engineering", ed. Addison-Wesley, second edition. Additional PFA lectures are available on the website edi.uniparthenope.it.
- written test;
- oral test.