E2 202: Random Processes (3:0)

Instructors

Anurag Kumar (ECE, IISc) and Rajesh Sundaresan (ECE and RBCCPS, IISc)

Teaching Assistants

Sudharshan TR
Sowmya S
TBD TBD TBD TBD

Lecture Hours

Lectures: Tuesdays and Thursdays, 14:00 - 15:30 hrs
Location: MP20 (Microelectronics and Photonics Building of the ECE Department)
First class: Tuesday 14:00 hrs, 05 August 2025, at ECE GJH

Lecture Plan

Lecture plan (PDF file).

Office Hours and Tutorial Sessions

Tutorials: Saturdays 10:00 - 11:30 hrs, handled by TAs
Location: MP20

Examinations

Mid-term 1: Saturday 13 September 2025, 10:00 - 11:30 hrs
Mid-term 2: Saturday 25 October 2025, 10:00 - 11:30 hrs
Final: TBA November 2025, TBA 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. Discrete time Markov chains, recurrence analysis, Foster's theorem. The Poisson process.

Course Grade

• 25% x 2 for the two mid-term examinations
  
• 50% Final examination
  
• Home work assignments will be given on a periodic basis.

Reference Text

• A. Kumar, Discrete Event Stochastic Processes: Lecture Notes for an Engineering Curriculum.

Supplementary Reading

• P. Bremaud, Introduction to Probabilistic Modeling, Springer-Verlag, 1988
• M. Loève, Probability Theory I, 4th edition, Springer-Verlag, 1977
• G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, Oxford University Press, 2020
• B. Hajek, Random Processes for Engineers, Cambridge University Press, 2015