E2 202, Fall 2022
Random Processes
Lectures
 02 Aug 2022: Lecture01 Sample and event space
 04 Aug 2022: Lecture02 Probability function
 09 Aug 2022: Lecture03 Independence of events
 11 Aug 2022: Lecture04 Random variables
 16 Aug 2022: Lecture05 Random vectors
 28 Aug 2022: Lecture06 Transformations of random vectors
 23 Aug 2022: Lecture07 Random processes
 25 Aug 2022: Lecture08 Expectation
 30 Aug 2022: Lecture09 Moments and L^p space
 01 Sep 2022: Lecture10 Correlation
 06 Sep 2022: Lecture11 Generating functions
 08 Sep 2022: Lecture12 Conditional expectation
 13 Sep 2022: Lecture13 Properties of conditional expectation
 15 Sep 2022: Lecture14 Almost sure convergence
 20 Sep 2022: Lecture15 $L^p$ convergence
 22 Sep 2022: Lecture16 Weak convergence
 27 Sep 2022: Lecture17 Tractable Random Processes
 29 Sep 2022: Lecture18 Stopping Times
 04 Oct 2022: Lecture19 Markov Chains
 06 Oct 2022: Lecture20 DTMC: Strong Markov Property
 11 Oct 2022: Lecture21 DTMC: Transient and recurrent states
 13 Oct 2022: Lecture22 DTMC: Communicating classes
 18 Oct 2022: Lecture23 DTMC: Invariant Distribution
 20 Oct 2022: Lecture24 Poisson point processes
 25 Oct 2022: Lecture25 Poisson point processes: Conditional distribution
 27 Oct 2022: Lecture26 Poisson point processes: Properties
 01 Nov 2022: Lecture27 Poisson processes on halfline
 03 Nov 2022: Lecture28 Poisson Processes: Compound
Homework
Homework discussions on Saturday 12:00 noon  01:00 pm after Quiz/Exams.
 04 Aug 2022: Homework01
 18 Aug 2022: Homework02
 01 Sep 2022: Homework03
 15 Sep 2022: Homework04
 29 Sep 2022: Homework05
 13 Oct 2022: Homework06
 27 Oct 2022: Homework07
 10 Nov 2022: Homework08
Tutorials
Monday 05:00 pm  06:30 pm
 08 Aug 2022: Tutorial01 Cardinality. Probability space. Limits of sets. Continuity of probability.
 15 Aug 2022: Tutorial02 Law of total probability. Independence of events. Conditional probability. Random variables.
 22 Aug 2022: Tutorial03 Random vectors. Transformation of random variables and random vectors.
 29 Aug 2022: Tutorial04 Random Processes. Expectation.
 05 Sep 2022: Tutorial05 Moments. Correlation. $L^p$ space. Inequalities.
 12 Sep 2022: Tutorial06 Generating functions. Conditional expectation.
 19 Sep 2022: Tutorial07 Almost sure convergence. Convergence in probability. BorelCantelli lemma.
 24 Sep 2022: Tutorial08 $L^p$ Convergence. Convergence in distribution. Problems on convergence of random variables.
 26 Sep 2022: Tutorial09 Law of large numbers. Central Limit theorem.
 03 Oct 2022: Tutorial10 Tractable random processes. Stopping times.
 10 Oct 2022: Tutorial11 Introduction to discrete time Markov chains.
 17 Oct 2022: Tutorial12 DTMC: Recurrent and transient states.
 24 Oct 2022: Tutorial13 DTMC: Communicating classes. Invariant distribution.
 31 Oct 2022: Tutorial14 Introduction to Poisson processes
 07 Nov 2022: Tutorial15 Thinning and superposition of Poisson processes
Tests
Quizzes: Saturday 11:30 am  12:00 noon
Midterms: Saturday 11:00 am  01:00 pm
Final: Wednesday 08:00 am  12:00 noon
 20 Aug 2022: Quiz01
 03 Sep 2022: Quiz02
 17 Sep 2022: Midterm01
 01 Oct 2022: Quiz03
 15 Oct 2022: Quiz04
 29 Oct 2022: Midterm02
 12 Nov 2022: Quiz05
 26 Nov 2022: Quiz06
 07 Dec 2022: Final
Grading Policy
Mid Term 1: 20
Mid Term 2: 20
Quizzes: 30
Final: 40
Class Participation: 10
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, conditional expectation, moment generating function, characteristic function
 Random vectors:
 joint distribution, conditional distribution, expectation, Gaussian random vectors.
 Convergence of random sequences:
 BorelCantelli 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.
 Bernoulli processes, independent increment processes, discrete time Markov chains, recurrence analysis,
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 RandomProcesses2022 using their iisc.ac.in email.
To join the right team, please use the code 4hycyqw.
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.
Midterms: Sat 11:00 am  01:00 pm.
HW Discussions: Sat 12:00 noon  01:00 pm.
Teaching Assistants
Avik Kar
Office: MP 221
Hours: By appointment.
Aniket Mukherjee
Office: ESE 316
Hours: By appointment.
Moonmoon Mohanty
Office: EC 2.16
Hours: By appointment.
Daniyal Khan
Office:
Hours: By appointment.
Aishwarya Anand
Office:
Hours: By appointment.
Shankul Saini
Office:
Hours: By appointment.
Duda Gayathri Reddy
Office:
Hours: By appointment.
Sriram G
Office:
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.