Degree Level

Probability and Statistics

To introduce the foundations of probability and statistics in the context of electronic systems.

Taught by Prof. Andrew Thangaraj

Code MA3101

Credits 4 Credits

Type Degree

Prerequisites None

12-Week Roadmap

Course Structure & Syllabus

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For details of standard term assessment timelines and exam structures, visit our Academics page.

Module 1

Probability space: Experiments, outcomes, sample space, events, Probability function, Axioms, Addition rule Computing probabilities, Conditional probability, Multiplication rule Bayes’ theorem, Total probability, Independence

Module 2

Discrete and continuous random variables: Bernoulli trials, Binomial distribution, Geometric distribution Discrete random variables, PMFs, Poisson distribution Multiple discrete random variables, Joint, Marginal and Conditional PMFs Functions of a discrete RV, Functions of multiple discrete RVs Expected value, Mean and Variance, Correlation and covariance From discrete to continuous distributions, Continuous CDFs, Densities, Common distributions Functions of a continuous RV, Expectations Multiple continuous RVs, Joint, Marginal and Conditional densities, Independence, Histograms

Module 3

Limit theorems: IID samples, Sample descriptive statistics, Empirical distribution, Normal sample statistics Sum of independent RVs, Law of large numbers, Central limit theorem.

Module 4

Estimation: MMSE estimators, Bayesian estimators, Maximum likelihood estimators

Reading List

Prescribed Books & References

Probability and Statistics, Morris DeGroot and Mark Schervish, Pearson; 4th ed., 2010
A Modern Introduction to Probability and Statistics, F. M. Dekking, C. Kraaikamp, H. P. Lopuhaa and L. E. Meester, Springer; 1st ed., 2005
Probability and Random Processes, G. Grimmett and D. Stirzaker, Oxford,3rd ed., 2001

Faculty & Experts

About the Instructors

Prof. Andrew Thangaraj

Professor , Electrical Engineering Department , IIT Madras

Faculty Webpage

Andrew Thangaraj received his B. Tech in Electrical Engineering from the Indian Institute of Technology (IIT) Madras in 1998 and Ph.D. in Electrical Engineering from the Georgia Institute of Technology, Atlanta, USA in 2003.

He was a post-doctoral researcher at the GTL-CNRS Telecom lab at Georgia Tech Lorraine, Metz, France from Aug 2003 till May 2004. Since 2004, he has been a faculty at the Department of Electrical Engineering, IIT Madras, where he is currently a professor.

His research interests are in the broad areas of information theory, error-control coding and information-theoretic aspects of cryptography. From Jan 2012 till Jan 2018, he served as Editor for the IEEE Transactions on Communications. From July 2018, he is an Associate Editor for the IEEE Transactions on Information Theory.

From Nov 2011, he has been one of the NPTEL coordinators for IIT Madras. At NPTEL, he has played a key role in the starting of online courses and certification. He is currently a National MOOCs coordinator for NPTEL under the SWAYAM project of the MHRD.

Prof. Andrew is also one of the coordinators for the IIT Madras Online BSc Degree Program, which was launched in June, 2020.

Other Courses by Instructor:

MA1101 • Math for Electronics I MA2101 • Math for Electronics II

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