E2 202, Fall 2019 | Parimal Parag

Random Processes

Lectures

05 Aug 2019: Lecture-01 Sample and Event Space
10 Aug 2019: Lecture-02 Probability Function
12 Aug 2019: Lecture-03 Independence of Events
14 Aug 2019: Lecture-04 Random Variables
19 Aug 2019: Lecture-05 Random Vectors
21 Aug 2019: Lecture-06 Expectation
26 Aug 2019: Lecture-07 Moments
28 Aug 2019: Lecture-08 Correlation
04 Sep 2019: Lecture-09 Conditional Expectation: Simple
07 Sep 2019: Lecture-10 Conditional Expectation: General
09 Sep 2019: Lecture-11 Transformations of Random Vectors
11 Sep 2019: Lecture-12 Characteristic Function
16 Sep 2019: Lecture-13 Gaussian Random Vectors
18 Sep 2019: Lecture-14 Almost sure convergence
23 Sep 2019: Lecture-15 L^p convergence
25 Sep 2019: Lecture-16 Weak convergence
30 Sep 2019: Lecture-17 Convergence
02 Oct 2019: Lecture-18 Random Processes: Independence
07 Oct 2019: Lecture-19 Tractable Random Processes
09 Oct 2019: Lecture-20 Markov Chains
14 Oct 2019: Lecture-21 DTMC: Random Representation Mapping
16 Oct 2019: Lecture-22 DTMC: Strong Markov Property
21 Oct 2019: Lecture-23 DTMC: Hitting and Recurrence Times
23 Oct 2019: Lecture-24 DTMC: Irreducibility and Aperiodicity
28 Oct 2019: Lecture-25 DTMC: Invariant Distribution
30 Oct 2019: Lecture-26 Poisson point processes
04 Nov 2019: Lecture-27 Poisson point processes: Properties
06 Nov 2019: Lecture-28 Poisson Processes: Equivalences
11 Nov 2019: Lecture-29 Poisson processes on half-line
13 Nov 2019: Lecture-30 Poisson Processes: Compound

Homework

15 Aug 2019: Homework-01
29 Aug 2019: Homework-02
13 Sep 2019: Homework-03
27 Sep 2019: Homework-04
12 Oct 2019: Homework-05
24 Oct 2019: Homework-06
08 Nov 2019: Homework-07

Tutorials

Tests

24 Aug 2019: Quiz-01
07 Sep 2019: Quiz-02
20 Sep 2019: Mid-term-01
05 Oct 2019: Quiz-03
19 Oct 2019: Quiz-04
02 Nov 2019: Mid-term-02
16 Nov 2019: Quiz-05
28 Nov 2019: Final (Hours: 09:00 am - 12:00 noon, Venue: MP 20, MP 30)

Grading Policy

Mid Term 1: 15 Mid Term 2: 15 Quizzes: 20 Final: 50

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.

Slack Information

Slack

Students can signup for course slack using their iisc.ac.in email at Slack signup. Add yourself to the public channel #rp-2019.

Instructor

Utpal Mukherji
Office: EC 1.02
Hours: By appointment.

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: Sat 11:35 am - 01:05 pm.

Teaching Assistants

Praneeth Kumar V.
Office: SP 2.23
Hours: By appointment.

Rooji Jinan
Office: EC 2.16
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.