E2 202: Random Processes (3:0)
August 2023
Instructors
Anurag Kumar (ECE, IISc) and Rajesh Sundaresan (ECE and RBCCPS, IISc)
Teaching Assistants
Janaky Murthy
Tejashree S
Mohammad Azfar
Amit Verma
Gollamudi Sai Srikar
Shravan Sridhar
Jaswanth Bodempudi
Lecture Hours
Lectures: Tuesdays and Thursdays, 14:00 - 15:30 hrs
Location: ECE GJH (Microelectronics and Photonics Building of the ECE Department)
First class: Thursday 14:00 hrs, 03 August 2023, at MP20
Lecture Plan
Office Hours and Tutorial Sessions
Office hour: Wednesdays 16:00 - 17:30 hrs
Location: Networks Lab, Ground Floor, ECE Building
Tutorials: Saturdays 10:00 - 11:30 hrs, handled by TAs
Location: ECE Golden Jubilee Hall, ECE Building
Examinations
Mid-term 1: Saturday 16 September 2023, 10:00 - 11:30 hrs
Mid-term 2: Saturday 28 October 2023, 10:00 - 11:30 hrs
Mid-term 3: Saturday 18 November 2023, 10:00 - 11:30 hrs
Final: Wednesday 06 December 2023, 14:00 - 17:00 hrs, as per SCC announcement
Course syllabus
The axioms of probability theory, continuity of probability, independence and conditional probability. Random variables and their distribution, functions of a random variable, expectation. Jointly distributed random variables, conditional distribution and expectation, Gaussian random vectors. Convergence of sequences of random variables, Borel-Cantelli Lemma, laws of large numbers and central limit theorem for sequences of independent random variables, Markov inequality. Definition of a random process, stationarity. Correlation functions of random processes in linear systems, power spectral density. Discrete time Markov chains, recurrence analysis, Foster's theorem. The Poisson process.
Course Grade
- 25% x 2 for the best two out of three mid-term examinations
- 50% Final examination
- Home work assignments will be given on a periodic basis.
Reference Texts
Supplementary Reading
- Pierre Bremaud, "Introduction to Probabilistic Modeling," Spring-Verlag, 1988
- M. Loève, Probability Theory I, 4th edition, Springer-Verlag, 1977