E2 202, Fall 2021

Random Processes


Lectures


Homework


Discussions on Saturday 12:00 noon - 01:00 pm after Quiz/Exams.

Tutorials


Monday 05:00 pm - 06:30 pm

Tests


  • 21 Aug 2021: Quiz-01
  • 04 Sep 2021: Quiz-02
  • 18 Sep 2021: Mid-term-01
  • 02 Oct 2021: Quiz-03
  • 16 Oct 2021: Quiz-04
  • 30 Oct 2021: Mid-term-02
  • 13 Nov 2021: Quiz-05
  • 09 Dec 2021: Final (Hours: 09:00 am - 12:00 noon)

Saturday 11:00 am - 12:00 noon

Grading Policy


Mid Term 1: 20
Mid Term 2: 20
Quizzes: 30
Final: 30
Class Participation: 10

Quiz Total = max(Quiz 1, Quiz 2) + max(Quiz 3, Quiz 4) + Quiz 5
Class participation is based on attendance and class interaction in lectures, tutorials, and homework discussions.

Course Syllabus


  • Probability Theory:
    • axioms, continuity of probability, independence, conditional probability.
  • Random variables:
    • distribution, transformation, expectation, moment generating function, characteristic function
  • Random vectors:
    • joint distribution, conditional distribution, expectation, Gaussian random vectors.
  • Convergence of random sequences:
    • Borel-Cantelli Lemma, laws of large numbers, central limit theorem, Chernoff bound.
  • 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-2021 using their iisc.ac.in email.
To join the right team, please use the code o3e13ho.
To be on the course team, you have to be formally registered for the course.
If you registered recently and wish to join the course team, please send a direct message on the Teams.

Instructor


Parimal Parag
Office: EC 2.17
Hours: By appointment.

Time and Location


Classroom: Auditorium 1, MP 20, ECE MP Building.
Hours: Tue/Thu 11:30am - 01:00pm.
Tutorial: Mon 05:00 pm - 06:30 pm.
Quizzes: Sat 11:00 am - 12:00 noon.
Mid-terms: Sat 11:00 am - 01:00 pm.
HW Discussions: Sat 12:00 noon - 01:00 pm.

Teaching Assistants


Rooji Jinan
Office: EC 2.16
Hours: By appointment.

Adwait Sharma
Hours: By appointment.

Ankita Koley
Hours: By appointment.

Vishnu Kunde
Hours: By appointment.

Aravind G
Hours: By appointment.

Hemanth Kongara
Hours: By appointment.

Anurag Chhetri
Hours: By appointment.

Navneet Kaur
Hours: By appointment.

Sachin Sampath
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.