E2 202, Fall 2020 | Parimal Parag

Random Processes

Lectures

05 Oct 2020: Lecture-01 Sample and Event Space
07 Oct 2020: Lecture-02 Probability Function
12 Oct 2020: Lecture-03 Independence of Events
14 Oct 2020: Lecture-04 Random Variables
19 Oct 2020: Lecture-05 Random Vectors
21 Oct 2020: Lecture-06 Transformations of Random Vectors
26 Oct 2020: Lecture-07 Expectation
28 Oct 2020: Lecture-08 Moments
02 Nov 2020: Lecture-09 Correlation
04 Nov 2020: Lecture-10 Conditional Expectation: Simple
09 Nov 2020: Lecture-11 Conditional Expectation: General
11 Nov 2020: Lecture-12 Characteristic Function
16 Nov 2020: Lecture-13 Almost sure convergence
18 Nov 2020: Lecture-14 L^p convergence
23 Nov 2020: Lecture-15 Weak convergence
25 Nov 2020: Lecture-16 Independent Random Processes
30 Nov 2020: Lecture-17 Stopping Times
02 Dec 2020: Lecture-18 Tractable Random Processes
07 Dec 2020: Lecture-19 Markov Chains
09 Dec 2020: Lecture-20 DTMC: Random Representation Mapping
14 Dec 2020: Lecture-21 DTMC: Hitting and Recurrence Times
16 Dec 2020: Lecture-22 DTMC: Irreducibility and Aperiodicity
21 Dec 2020: Lecture-23 DTMC: Invariant Distribution
23 Dec 2020: Lecture-24 Poisson point processes
28 Dec 2020: Lecture-25 Poisson point processes: Conditional distribution
30 Dec 2020: Lecture-26 Poisson point processes: Properties
04 Jan 2020: Lecture-27 Poisson processes on half-line
06 Jan 2020: Lecture-28 Poisson Processes: Compound

Homework

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

02 Oct 2020: Homework-01
16 Oct 2020: Homework-02
30 Oct 2020: Homework-03
13 Nov 2020: Homework-04
27 Nov 2020: Homework-05
11 Dec 2020: Homework-06
25 Dec 2020: Homework-07

Tutorials

09 Oct 2020: Tutorial-01 Cardinality, sigma algebras, and the probability function
16 Oct 2020: Tutorial-02 Conditional probability, independence, random variables, and distribution functions
23 Oct 2020: Tutorial-03 Random vectors and functions of random variables
30 Oct 2020: Tutorial-04 Expectations and some inequalities
06 Nov 2020: Tutorial-05 Conditional distribution and conditional expectation
13 Nov 2020: Tutorial-06 Characteristic functions and jointly Gaussian random variables
20 Nov 2020: Tutorial-07 Convergence of random variables
21 Nov 2020: Tutorial-08 Problems on convergence of random variables
27 Nov 2020: Tutorial-09 Weak convergence and limit theorems
04 Dec 2020: Tutorial-10 Introduction to random processes
11 Dec 2020: Tutorial-11 Introduction to Markov chains
18 Dec 2020: Tutorial-12 Recurrence of Markov chains
25 Dec 2020: Tutorial-13 Invariant distribution of Markov chains

Tests

17 Oct 2020: Quiz-01
31 Oct 2020: Quiz-02
14 Nov 2020: Mid-term-01 (11:30 am - 01:30 pm)
28 Nov 2020: Quiz-03
12 Dec 2020: Quiz-04
26 Dec 2020: Mid-term-02 (11:30am - 01:30 pm)
09 Jan 2020: Quiz-05
09 Dec 2020: Final (Hours: 09:00 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-2020 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: MW 09:30am - 11:00am.
Tutorial: F 09:30 am - 11:00 am.
Quizzes: Sat 11:00 am - 12:00 noon.
Mid-terms: Sat 11:30 am - 01:30 pm.