### Basic Information

**Course Code**: EE 734**Course Name**: Advanced Probability and Random Processes for engineers**Course Offered In**: 2023-2024**Semester Season**: Spring**Instructors**: Prof. Vivek Borkar**Prerequisites**: EE 325 Some background of Markov chains and Martingales is appreciated but not needed.**Difficulty (1 being easy and 5 being tough)**: 4

### Course Content

Probability spaces, Random variables, Conditional probability, Uniform integrability, Expectation, Convergence, Martingales, Markov chains

### Feedback on Lectures

The course starts from a very basic EE 325 level and has a relatively easier first half comprising of probability spaces, random variables, expectation, conditional expectation, etc. Prof Borkar uses a fixed set of slides to teach every year. While the lectures were a little monotonous, the slides are packed with everything you need to ace this course. The latter half of the course is relatively tough and covers Martingales and Markov chains. Prof Borkar regularly provides exercises which must be thoroughly solved to gain a better understanding of the course content.

### Feedback on Evaluations

There was no endsem or midsem for our batch. Evaluation was as per our performance in 3 open-book quizzes where we could refer to hard copies of slides and notes (digital notes and devices not allowed) — covering probability basics in the first, Martingales in the second and Markov chains in the third. Solving the quiz papers was a thrilling experience. Questions will not be straightforward or formula-based. Having an in-depth understanding of the subject and a good exposure to writing proofs comes in handy for this course.

### Study Material and Resources

- Prof’s slides and exercise sheets are a must.
- Measure & Probability — Athreya & Sunder
- First course in probability — Kai Lai Chung
- Probability — Breiman
- Introduction to Probability — K.R. Parthasarathy

### Follow-up Courses

-Can be taken with EE 6106: Online learning and Optimisation (runs in the same semester) -Any course on measure theory

### Final Takeaway

Take this course if you love the thrill of old school mathematics, or wish to expand your knowledge of probability theory. The course is difficult and does not have easy grades. If you like the idea struggling for 2 hours with daunting math problems, this course is for you!