E2 202: Random Processes (3:0)

Instructors

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

Teaching Assistants

Chirayata Bhattacharyya
Arpan Das
Manali Dutta
Abhivyakti Khare
Goutham C Krishnan
Writtik Majumder
Janaky Murthy
Ramansh Sharma

Lecture Hours

Lectures: Tuesdays and Thursdays, 14:00 - 15:30 hrs
Location: ECE GJH (Microelectronics and Photonics Building of the ECE Department)
First class: Tuesday 14:00 hrs, 06 August 2024, at ECE GJH

Lecture Plan

Lecture plan (PDF file).

Office Hours and Tutorial Sessions

Office hour: Wednesdays 16:00 - 17:30 hrs
Location: ECE 1.08

Tutorials: Saturdays 10:00 - 11:30 hrs, handled by TAs
Location: ECE Golden Jubilee Hall, ECE Building

Examinations

Mid-term 1: Saturday 31 August 2024, 10:00 - 11:30 hrs
Mid-term 2: Saturday 28 September 2024, 10:00 - 11:30 hrs
Mid-term 3: Saturday 26 October 2024, 10:00 - 11:30 hrs
Final: Tuesday 26 November 2024, 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

• Anurag 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