### EE 325 – PROBABILITY AND RANDOM PROCESSES

**Course offered in:**

Autumn 2020

**Instructors:**

Prof BK Dey

Prof Nikhil Karamchandani

**Course Content:**

This is an important introductory course to probability theory that lays the foundation for many communications and applied probability courses. The course contents are:

– Set theory review

– Probability space, conditional probability

– Random variables, cumulative distribution functions

– Random vectors, joint distributions

– Covariance and correlation functions

– Minimum mean square error estimation

– Transformations of random vectors

– Generating functions, characteristic functions

– Multivariate normal distributions and jointly Gaussian random variables

– Concentration bounds

– Convergence of sequence of random variables

– Random processes-types, continuity, differentiation, integration, ergodicity, KL expansion

– LTI systems

– White Gaussian noise

**Prerequisites:**

No strict prerequisites

**Feedback on Lectures:**

Videos with around 2-3 hours of content were uploaded every week. The lectures were good and the entire course was well structured. Both the professors explained very well and I rarely found the need to go beyond the content that they provided to understand. The in video questions provided on Moodle were pretty useful in understanding the lecture. Supplementary material was provided each week in the live interaction session which elaborates upon some concept covered in the previous week which tied up some loose ends for me.

The professors are very open to doubts in the live interaction session and I would encourage anyone taking the course to attend these and make full use of them as the course does get harder progressively. They also took attendance a bit seriously even though it was an online sem so I would highly recommend showing up for live interaction sessions.

**Feedback on Tutorials, Assignments and Exams:**

There were tutorial sheets provided every week which were discussed during the tutorial hour. Detailed solutions were posted at the end of the tutorial but stopped towards the end after the professors observed low attendance.

There were 4 assignments worth 20%, weekly Moodle quizzes worth 20% (best 8/11) and an endsem of 60%. There was no midsem because it was the first online sem but I would expect there to be midsems in following offerings of this course. The weekly Moodle quizzes were pretty straightforward and mostly just aimed to test whether you’ve seen the recorded lectures at all. The assignments were harder than the weekly quizzes but can be done easily if you’re up to date with the lectures. The questions in the endsem were pretty much similar to those given in the tutorials and assignments. Doing the tutorials and assignments on your own as well as understanding the lecture content properly and clearing any doubts as early as possible is enough to do well in my opinion.

**Difficulty:**

This is probably the most rigorous EE core course (definitely not as much as math courses) and hence might be a bit hard to get used to. I do think putting in efforts every week and not letting content (lectures or tutorials) pile up for the week before the exam is enough to understand the course and get a good grade.

**Study Material and References:**

References suggested by the professors:

Probability and Random Processes, Grimett and Stirzaker

Probability, random variables and stochastic processes, Papoulis and Pillai

First course in probability, Sheldon Ross

1000 exercises in probability, Grimmett and Stirzaker

Notes were provided along with the lectures and they are pretty much sufficient to understand most of the concepts being taught. If you have time can refer to any of these references. The professors usually mention which part of what book they referred to for each topic, which is pretty useful if anyone would want to read more.

**Advanced courses that can be taken after this:**

This course is a prerequisite for most applied probability or communications courses like EE708 (Information Theory), EE605 (Error correcting codes), EE736 (Introduction to Stochastic Optimization), EE621 (Markov chains and Queuing Systems) and many more.

**Takeaways from the course:**

For anyone interested in pursuing applied probability, this course is very important. Getting a good grasp of the topics at the end related to Gaussian noise and LTI systems would be very helpful to anyone interested in communications and signal processing.

Review by – Fathima Zarin Faizal (180070018@iitb.ac.in)

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