E2 202, Fall 2021

Random Processes

Lectures

• 03 Aug 2021: Lecture-01 Sample and event space
• 05 Aug 2021: Lecture-02 Probability function
• 10 Aug 2021: Lecture-03 Independence of events
• 12 Aug 2021: Lecture-04 Random variables
• 17 Aug 2021: Lecture-05 Random vectors
• 19 Aug 2021: Lecture-06 Transformations of random vectors
• 24 Aug 2021: Lecture-07 Random processes
• 26 Aug 2021: Lecture-08 Expectation
• 31 Aug 2021: Lecture-09 Moments and L^p space
• 02 Sep 2021: Lecture-10 Correlation
• 07 Sep 2021: Lecture-11 Generating functions
• 09 Sep 2021: Lecture-12 Almost sure convergence
• 14 Sep 2021: Lecture-13 L^p convergence
• 16 Sep 2021: Lecture-14 Weak convergence
• 21 Sep 2021: Lecture-15 Conditional expectation
• 23 Sep 2021: Lecture-16 Properties of conditional expectation
• 28 Sep 2021: Lecture-17 Tractable Random Processes
• 30 Sep 2021: Lecture-18 Stopping Times
• 05 Oct 2021: Lecture-19 Markov Chains
• 07 Oct 2021: Lecture-20 DTMC: Strong Markov Property
• 12 Oct 2021: Lecture-21 DTMC: Transient and recurrent states
• 14 Oct 2021: Lecture-22 DTMC: Communicating classes
• 19 Oct 2021: Lecture-23 DTMC: Invariant Distribution
• 21 Oct 2021: Lecture-24 Poisson point processes
• 26 Oct 2021: Lecture-25 Poisson point processes: Conditional distribution
• 28 Oct 2021: Lecture-26 Poisson point processes: Properties
• 02 Nov 2021: Lecture-27 Poisson processes on half-line
• 04 Nov 2021: Lecture-28 Poisson Processes: Compound

Homework

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

• 09 Aug 2021: Homework-01
• 23 Aug 2021: Homework-02
• 06 Sep 2021: Homework-03
• 20 Sep 2021: Homework-04
• 04 Oct 2021: Homework-05
• 18 Oct 2021: Homework-06
• 01 Nov 2021: Homework-07

Tutorials

Monday 05:00 pm - 06:30 pm

• 08 Aug 2021: Tutorial-01 Cardinality. Sample space. Sigma algebras. Limits of sets.
• 16 Aug 2021: Tutorial-02 Law of total probability. Random variables and their measurability.
• 23 Aug 2021: Tutorial-03 Examples of random variables and random vectors. Transformation of random vectors.
• 28 Aug 2021: Tutorial-04 Expectations and some inequalities
• 04 Sep 2021: Tutorial-05 Conditional distribution and conditional expectation
• 11 Sep 2021: Tutorial-06 Characteristic functions and jointly Gaussian random variables
• 18 Sep 2021: Tutorial-07 Convergence of random variables
• 25 Sep 2021: Tutorial-08 Problems on convergence of random variables
• 02 Oct 2021: Tutorial-09 Weak convergence and limit theorems
• 09 Oct 2021: Tutorial-10 Introduction to random processes
• 16 Oct 2021: Tutorial-11 Introduction to Markov chains
• 23 Oct 2021: Tutorial-12 Recurrence of Markov chains
• 30 Oct 2021: Tutorial-13 Invariant distribution of Markov chains
• 06 Nov 2021: Tutorial-14 Poisson Processes
• 13 Nov 2021: Tutorial-15 Poisson Processes

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.