E2 202: Random Processes (3:0)

Instructor

Rajesh Sundaresan (ECE)

Teaching Assistants

Sowmya S
Ram Rathan KR
Tithi Chethan Mahajani
Dwaipayan Halder
Yash Pandey

Lecture Hours

Lectures: Tuesdays and Thursdays, 14:00 - 15:30 hrs
Location: MP20 (Microelectronics and Photonics Building of the ECE Department)
First class: Tuesday 04 August 2026, 14:00 - 15:30 hrs

Lecture Plan

Lecture plan (PDF file).

Office Hours and Tutorial Sessions

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

Problem Sets

• Problem Set 1, Discussion 08 August 2026
• Problem Set 2, Discussion 15,17,20 August 2026
• Problem Set 3, Discussion 29 August 2026
• Problem Set 4, Discussion 03,12 September 2026
• Problem Set 5, Discussion 19 September 2026
• Problem Set 6, Discussion 03 October 2026
• Problem Set 7, Discussion 08 October 2026
• Problem Set 8, Discussion 24 October 2026
• Problem Set 9, Discussion 05 November 2026

Examinations

Practice test: Thursday 27 September 2026, 18:00 - 19:30 hrs
Mid-term 1: Saturday 05 September 2026, 10:00 - 11:30 hrs
Mid-term 2: Saturday 10 October 2026, 10:00 - 11:30 hrs
Mid-term 3: Saturday 07 November 2026, 10:00 - 11:30 hrs
Final: Friday 27 November 2026, 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. Discrete time Markov chains, recurrence analysis, Foster's theorem. The Poisson process.

Course Grade

• 50% From three 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