EE 5110: Probability Foundations for Electrical Engineers

July-November 2017

Instructor: Krishna Jagannathan, Assistant Professor

 

TAs:

·      Pawan Poojary: ee15s025@ee.iitm.ac.in

·      Ramakrishnan S: ee12d036@ee.iitm.ac.in

·      Vishnu M: ee16s301@ee.iitm.ac.in

·      Sapana Chaudhary: ee15s300@ee.iitm.ac.in

Slot: E

 

Classroom: ESB 350

 

 

NPTEL Video Course:

The 2014 offering of this course has been recorded and uploaded on NPTEL (National Program on Technology Enhanced Learning). 

 
Syllabus
 
Videos: NPTEL :: Electrical Engineering
 
The YouTube channel of the course can be found here.
 
LaTeX notes for the course can be found here.
 
The videos are not optimised for the online format in anyway; indeed they are just videos of live classes taught at IIT Madras. I hope that you find the lectures useful/interesting! I welcome comments and feedback, of course!

 

This is a graduate level class on probability theory, geared towards students who are interested in a rigorous development of the subject. It is likely to be useful for students specializing in communications, networks, signal processing, stochastic control, machine learning, and related areas. In general, the course is not so much about computing probabilities, expectations, densities etc. Instead, we will focus on the ‘nuts and bolts’ of probability theory, and aim to develop a more intricate understanding of the subject. For example, emphasis will be placed on deriving and proving fundamental results, starting from the basic axioms.

 

Prerequisites: There will be no official pre-requisites. Although the course will build up from the basics, it will be taught at a fairly sophisticated level. Familiarity with concepts from real analysis will also be useful. Perhaps the most important prerequisite for this class is an intangible one, namely mathematical maturity.

 

Course Contents:

 

·             Probability Spaces, σ-algebras, events, probability measures

·             Borel Sets and Lebesgue measure

·             Conditioning, Bayes’ rule

·             Independence

·             Borel-Cantelli Lemmas

·             Measurable functions, random variables

·             Distribution functions, types of random variables

·             Joint distributions, transformation of random variables

·             Integration, expectation, covariance, correlation

·             Conditional expectation and MMSE estimation

·             Monotone convergence theorem, Dominated convergence theorem, Fatou’s lemma

·             Transforms (Moment generating function, characteristic function)

·             Concentration Inequalities

·             Jointly Gaussian random variables

·             Convergence of random variables, various notions of convergence

·             Central limit theorem

·             The laws of large numbers (the weak and strong laws)

 

References:

1.     Scribed notes.

2.     Probability and Random Processes by Geoffrey R. Grimmett and David R. Stirzaker. Oxford University Press, 3rd edition, 2001.

3.     MIT OCW.

All Tutorials, Handouts and Solutions will be uploaded to the course moodle.