Unit PROBABILITY THEORY
- Course
- Computer science and electronic engineering
- Study-unit Code
- 70A00056
- Curriculum
- In all curricula
- Teacher
- Paolo Carbone
- Teachers
-
- Paolo Carbone
- Hours
- 54 ore - Paolo Carbone
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2021/22
- Learning activities
- Caratterizzante
- Area
- Ingegneria elettronica
- Academic discipline
- ING-INF/07
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Introduction to probability theory: continuous, discrete and mixed random variables. Probability density functions. Probability distribution functions. Joint random variables. Introduction to stochastic processes: definitions, autocorrelation and autocovariance functions. Fundamentals of stochastic processes.
- Reference texts
- Roy. D. Yates, David J. Goodman, Probability and Stochastic Processes, John Wiley & Sons Inc; 2nd International Edition, 2004.
Handouts by the instructor. - Educational objectives
- The objective of this module is to provide the students with the knowledge to correctly apply probability theory and measurement theory. At the end of this class the student will have learned:
- the concept of continuous and discrete random variable and its PDF and CDF
- the concept of function of a random variable
- the concept of joint random variables and vector of random variables
- the concept of function of two random variables
- the concept of stochastic process and of its general properties
Moreover, he will be able to:
- solve exercises that require modeling using discrete, continuous and mixed random variables
- solve exercises using the concept of stochastic process - Prerequisites
- Calculus I is mandatory. Students must also be able to perform simple mathematical modeling in two dimensions and capable to solve simple double integrals.
- Teaching methods
- Frontal lectures at the blackboard. Students are expected to provide active participation and show autonomous study capabilities. Proficiency in solving exercises can only be developed by complementing attendance of lectures with dedicated sessions in the solution of exercises at home.
- Other information
- Information about available services for people with disabilities and/or with learning disabilities, see:
http://www.unipg.it/disabilita-e-dsa - Learning verification modality
- Written and oral tests. The written test requires solving two exercises (7 and 8 points each) and in answering 15 quizzes with 4 possible answers, of which only one is the correct one.
To each correct quiz answer 1 point is assigned. Wrong answers results in minus half a point. The oral examination covers all course content program and consists both in questions about the theory and in the solution of exercises. Its lenght is about 20-25 minutes. The final grade is based on both grades in the written and oral examinations. - Extended program
- Set theory. Sample spaces and random events. How to assign probabilities: classical, empirical and subjective approach. Conditional probability. Total probability theorem. Bayes theorem. Combinatorial calculus: permutations, dispositions, combinations. Random variables. Cumulative3 distribution function. Probability density function. Discrete random variables: Bernoulli, geometrical, binomial, Pascal, uniform discrete. Mode, median, expected value. Transformed random variables. Expected value of a transformed random variable. Variance and standard deviation. Central and non-central moments. Conditional mass probability. Continuous random variables. Cumulative and density functions. Expected value. Probability models: uniform, exponential, Gaussian. Mixed random variables. Transformed continuous random variables. Conditional continuous random variables. Couples of random variables. Marginal probability density functions. Transformation of two random variables. Rayleigh and Rice probability models. Orthogonal random variables. Correlation, covariance. Correlation coefficient. Conditioning two random variables. Random vectors. Gaussian random vectors. Central limit theorem. De-Moivre Laplace formula. Introduction to stochastic processes. Moments. Wide-sense and strict-sense stationary random processes. Ergodic processes.