## Random Processes

### Homework

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

### Tutorials

Monday 05:00 pm - 06:30 pm

### Tests

Quizzes: Saturday 11:30 am - 12:00 noon
Mid-terms: Saturday 11:00 am - 01:00 pm
Final: Wednesday 08:00 am - 12:00 noon

• 20 Aug 2022: Quiz-01
• 03 Sep 2022: Quiz-02
• 17 Sep 2022: Mid-term-01
• 01 Oct 2022: Quiz-03
• 15 Oct 2022: Quiz-04
• 29 Oct 2022: Mid-term-02
• 12 Nov 2022: Quiz-05
• 26 Nov 2022: Quiz-06
• 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:
• 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-2022 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.
Mid-terms: 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.