E2 202 : Random Processes, Fall 2017
Lectures
Homeworks
Tutorials
05 Aug 2017: Sample space, sigma algebra, example constructions of sigma algebras, “infinitely often” and “all but finitely many” events
12 Aug 2017: Probability measure, continuity of probability, independence and conditional independence  examples and exercises
19 Aug 2017: Borel sigma algebra, random variables, CDF and its properties, construction of CDF from a probability measure, example constructions of random variables with respect to various sigma algebras  exercises
24 Aug 2017: Random variables  examples and exercises
31 Aug 2017: Expectation of random variables, an overview of Lebesgue integrals
06 Sep 2017: Joint CDF, marginals, conditional distribution, calculating expectation of some commonly used random variables  exercises
09 Sep 2017: Simulation of random variables, finiteness of moments, expectation in terms of CDF for nonnegative random variables
16 Sep 2017: Transformation of random variables  exercises
23 Sep 2017: Moment generating function, characteristic function, Gaussian random vectors  exercises
28 Sep 2017: Convergence of real sequences, convergence of sequence of random variables, BorelCantelli Lemma
03 Oct 2017: Convergence of real sequences, convergence of sequence of random variables, BorelCantelli Lemma (contd.)  exercises
14 Oct 2017: Conditional expectations, an overview of stochastic processes, finite dimensional distributions and filtrations
19 Oct 2017: Stopping times, stopping time sigma algebra, strong Markov property
28 Oct 2017: Discussion  exercises
04 Nov 2017: Discrete Time Markov Chains and properties  examples
07 Nov 2017: Discrete Time Markov Chains: Invariant distributions
11 Nov 2017: Discussion of mid term 1 and mid term 2 solution
18 Nov 2017: Poisson processes  characterizations, interarrival times
25 Nov 2017: Poisson processes  merging, splitting, nonhomogeneous and compound; Strong Markov property, Order statistics, summary of the course
Tests
31 Aug 2017: Quiz 1 Solution
09 Sep 2017: Quiz 2 Solution
21 Sep 2017: Mid Term 1
11 Oct 2017: Quiz 3 Solution
28 Oct 2017: Quiz 4 Solution
09 Nov 2017: Mid Term 2
22 Nov 2017: Quiz 5 Solution
07 Dec 2017: Final (Hours: 2pm  5pm, Venue: EC 1.07, 1.08)
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.
Random vectors: joint distribution, conditional distribution, expectation, Gaussian random vectors.
Convergence of random sequences: BorelCantelli 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/GitHub Information
Slack
Students can signup for slack using their iisc.ac.in email at Slack signup.
Instructors
Utpal Mukherji
Office: ECE 1.02
Parimal Parag
Office: ECE 2.17
Hours: Fri 02:00 pm  03:00 pm.
Time and Location
Classroom: ECE 1.08, Main ECE Building.
Class Hours: Tue/Thu 02:00 pm  03:30 pm.
Tutorial Hours: Sat 10:00 am  11:30 am.
Teaching Assistants
Karthik P N: periyapatna@iisc.ac.in
Office: MP 327
Office Hours: Mon/Wed 03:45 pm  04:45pm
Sahasranand KR: sahasranand@iisc.ac.in
Textbooks
Probability and Random Processes, Geoffrey Grimmett and David Stirzaker, 3rd edition, 2001.
Discrete Event Stochastic Processes, Anurag Kumar, Department of Electrical Communication Engineering, Indian Institute of Science
Random Processes for Engineers, Bruce Hajek, 2014.
Introduction to Probability, Dimitri P. Bertsekas and John N. Tsitsiklis, 2nd edition, 2008.
A First Course in Probability, Sheldon M. Ross, 2013.
Probability Essentials, Jean Jacod & Philip Protter, Springer, 2004.
Probability, Random processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance, Kobayashi, Hisashi, Brian L. Mark, and William Turin, Cambridge University Press, 2011.
