Probability Foundations for Electrical Engineers

By Prof. Krishna Jagannathan   |   IIT Madras
Learners enrolled: 794
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.

INTENDED AUDIENCE
M.Tech/M.S/PhD students, who plan to specialize in communications, networks, signal processing, stochastic control, machine learning, or related areas.
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.
INDUSTRIES  SUPPORT     : Research labs
Summary
 Course Status : Ongoing Course Type : Core Duration : 12 weeks Start Date : 26 Jul 2021 End Date : 15 Oct 2021 Exam Date : 23 Oct 2021 IST Enrollment Ends : 09 Aug 2021 Category : Electrical, Electronics and Communications Engineering Credit Points : 3 Level : Postgraduate

Course layout

Week 1: Introduction, Cardinality and Countability, Probability Space
Week 2: Properties of Probability Space, Discrete Probability Space, Generated \sigma-algebra
Week 3:  Borel sets, Caratheodory’s extension theorem, Lebesgue Measure, Infinite coin toss model
Week 4: Conditional probability, Independence, Borel-Cantelli Lemmas
Week 5: Random variables, Distribution function, Types of random variables
Week 6: Discrete Random variables, Continuous random variables, Singular random variables
Week 7:  Several random variables, joint distribution, independent random variables
Week 8: Transformation of random variables
Week 9: Integration and Expectation, properties of integrals, Monotone convergence, Dominated convergence, Expectation over different spaces
Week 10:Variance, covariance, and conditional expectation
Week 11: Transform techniques: moment generating function, characteristic function
Week 12:Convergence of random variables, Laws of large numbers, Central limit theorem

Books and references

1. Probability and Random Processes by Geoffrey R. Grimmett and David R. Stirzaker. Oxford University Press, 3rd edition, 2001.
2. Probability with Martingales by D. Williams, Cambridge University Press, 1991.
3. A First Look at Rigorous Probability Theory by J. Rosenthal, World Scientific Publishing Co Pte Ltd; 2nd Revised edition, 2006.

Prof. Krishna Jagannathan

Krishna Jagannathan obtained his B. Tech. in Electrical Engineering from IIT Madras in 2004, and the S.M. and Ph.D. degrees in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology (MIT) in 2006 and 2010 respectively. During 2010-2011, he was a visiting post-doctoral scholar in Computing and Mathematical Sciences at Caltech, and an off-campus post-doctoral fellow at MIT. Since November 2011, he has been with the Department of Electrical Engineering, IIT Madras, where he is currently an Associate Professor.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team