Course Information Package
|Course Unit Title||RANDOM VARIABLES AND STOCHASTIC PROCESSES|
|Course Unit Code||AEEE503|
|Course Unit Details||MSc Electrical Engineering (Required Courses) -|
|Number of ECTS credits allocated||7|
|Learning Outcomes of the course unit||By the end of the course, the students should be able to:|
|Mode of Delivery||Face-to-face|
|Recommended optional program components||NONE|
� Introduction to Probability : Overview of set theory. Sample Spaces, Events, Sigma-fields, Axiomatic Definition of Probability, Joint Probabilities, Conditional Probabilities, Total Probability,
� Random Variables: Definition of Random Variables, Probability distribution function, Probability density function, Conditional and joint distributions and densities, Functions of Random Variables, Expected Value of a Random Variable, Conditional Expectations, Moments, Joint Moments, Moment Generating Functions, Characteristic Functions.
� Revision on Linear Algebra: Multiplication, Linear Dependence, Determinants, Eigenvalues, Eigenvectors, Positive Definite Matrices, Causal Factorization, Spectral Resolution.
� Second Moment Descriptions: Covariance, Correlation, Linear Transformation of Random Vectors, the Simulation Problem, Gaussian Functions, Gaussian Characteristic Functions, Linear Transformations, The probability density function of a Gaussian random vector.
� Applications using Second Order Information: Hypothesis Testing with second order information, Correlation Detection in Additive Noise, Whitening, Bayes decision theory, Minimization of probability of error, Likelihood ratio tests, Mean Square Estimation.
� Stochastic Processes: Definition of Random Processes, Examples of Random Processes, Phase Shift Keying, Wiener Process, Markov Processes, Poisson Processes, Stationarity, Power Spectral Density, Kalman Filtering.
|Recommended and/or required reading:|
|Planned learning activities and teaching methods|
� Students are taught the course through lectures (3 hours per week) in classrooms or lectures theatres, by means of traditional tools or using computer demonstration.
� Auditory exercises, where examples regarding matter represented at the lectures, are solved and further, questions related to particular open-ended topic issues are compiled by the students and answered, during the lecture or assigned as homework.
� Topic notes are compiled by students, during the lecture which serve to cover the main issues under consideration and can also be downloaded from the lecturer’s webpage. Students are also advised to use the subject’s textbook or reference books for further reading and practice in solving related exercises. Tutorial problems are also submitted as homework and these are solved during lectures or privately during lecturer’s office hours. Further literature search is encouraged by assigning students to identify a specific problem related to some issue, gather relevant scientific information about how others have addressed the problem and report this information in written or orally.
� Students are assessed continuously and their knowledge is checked through tests with their assessment weight, date and time being set at the beginning of the semester via the course outline.
� Students are prepared for final exam, by revision on the matter taught, problem solving and concept testing and are also trained to be able to deal with time constraints and revision timetable.
� The final assessment of the students is formative and summative and is assured to comply with the subject’s expected learning outcomes and the quality of the course.
|Assessment methods and criteria|
|Language of instruction||English|