E2 202o, Fall 2025

Random Processes

Lectures

Homework

Tutorials

Homework discussions and Quizzes Saturday 02:00 pm - 03:30 pm

Tests

Quizzes: Saturday 03:00 pm - 03:30 pm
Mid-terms: Saturday 02:00 pm - 03:30 pm
Final: Wednesday 08:00 am - 12:00 noon

  • 20 Aug 2025: Quiz-01
  • 03 Sep 2025: Quiz-02
  • 17 Sep 2025: Mid-term-01
  • 01 Oct 2025: Quiz-03
  • 15 Oct 2025: Quiz-04
  • 29 Oct 2025: Mid-term-02
  • 12 Nov 2025: Quiz-05
  • 26 Nov 2025: Quiz-06
  • 07 Dec 2025: Final

Grading Policy

Quizzes: 30
Mid Term: 30
Final: 40

Class participation is based on attendance and class interaction in lectures, tutorials, and homework discussions.

Course Syllabus

  • Mathematical Preliminaries:
    • Sets, Functions, Cardinality
  • Probability Theory:
    • axioms, continuity of probability, independence, conditional probability
  • Random variables:
    • distribution, transformation, expectation, conditional expectation, moment generating function, characteristic function
  • Random vectors:
    • joint distribution, conditional distribution, expectation, Gaussian random vectors.
  • Convergence of random sequences:
    • Borel-Cantelli Lemma, almost sure convergence, convergence in probability, convergence in $L^p$, weak convergence, laws of large numbers, central limit theorem, $L^1$ convergence theorems
  • Discrete time random processes:
    • ergodicity, strong ergodic theorem, definition, stationarity, correlation functions in linear systems, power spectral density.
  • Structured random processes:
    • Bernoulli processes, independent increment processes, discrete time Markov chains, recurrence analysis, Foster’s theorem, reversible Markov chains, the Poisson process.

Course Description

Basic mathematical modeling is at the heart of engineering. In both electrical and computer engineering, uncertainty can be modeled by appropriate probabilistic objects. This foundational course will introduce students to basics of probability theory, random variables, and random sequences.

Teams Information

We will use Microsoft Teams for all the course related communication.
Please do not send any email regarding the course.
Students can signup for Microsoft Teams Random-Processes-2025 using their iisc.ac.in email.

Instructor

Parimal Parag
Office: EC 2.17
Hours: By appointment.

Time and Location

Hours: Tue/Thu 04:00 pm - 03:30pm.
Tutorial: Sat 02:00 pm - 03:30 pm.
Quizzes: Sat 03:00 pm - 03:30 pm.
Mid-term: Sat 02:00 pm - 03:30 pm.

Teaching Assistants

Aniket Mukherjee
Office: ESE 316
Hours: By appointment.

Moonmoon Mohanty
Office: EC 2.16
Hours: By appointment.

Nomula Taraka Sada Siva Srinivas
Office: EC 2.16
Hours: By appointment.

Venkatesan D
Office: EC 2.16
Hours: By appointment.

Textbooks

Probability and Random Processes, Geoffrey Grimmett and David Stirzaker, 3rd edition, 2001.

Probability and Random Processes: With Applications to Signal Processing and Communications, Scott L. Miller and Donald G. Childers, 2nd Edition, 2012.

Random Processes for Engineers, Bruce Hajek, 2014.

Introduction to Probability, Dimitri P. Bertsekas and John N. Tsitsiklis, 2nd edition, 2008.

Discrete Event Stochastic Processes, Anurag Kumar.