### EE 325 – PROBABILITY AND RANDOM PROCESSES

**Session**

2018-19

**Instructor**

D. Manjunath

**Course Content**

Probability and Random Processes is a very fundamental course that will give you a solid insight into statistics and dealing with time varying functions. It finds huge applications in Information theory, Signal Processing and Financial markets. The instructor covered the first four chapters from the book by Bruce Hajek along with a few extra topics. The course content is organized as follows:

1) The initial couple of weeks will deal with revising concepts from EE 223. This will mainly involve going through the basics of Probability theory and its axioms.

2) The next part of the course deals with various inequalities and asymptotic behavior of large numbers. Convergence of sequences, Law of Large numbers, Central limit theorem and Chernoff bounds were the important topics covered.

3) The instructor took a digression from the book and dived into the concepts of Maximum Likelihood Estimation (MLE) and Maximum a posteriori Estimation (MAP). This was followed by Monte Carlo simulations and Importance sampling.

4) The course dealt with estimators and the orthogonality principle. We were introduced to Linear and Non Linear estimators for minimum mean square error estimation. The instructor devoted considerable amount of time to Kalman Filtering.

5) The last part of the course introduced Random processes and ran us through its fundamentals. Concepts like Gambler’s ruin and Poisson Processes were also taught. The course ended with covering Fourier transform as a tool between Autocorrelation functions and Power Spectral density.

**Prerequisite**

Although not a hard pre-requisite EE 223 – Data Analysis and Interpretation will form a good base to this course.

**Feedback on the lectures –**

The lectures were extremely insightful and the instructor taught with great enthusiasm. Attending lectures will be very important for this course. The text for the course is a bit convoluted and attending the lectures will give a massive support in understanding and solving the questions in the text along with the tutorials. Moreover the instructor also took attendance at the end of every class.

**Feedback on Assignments/Tutorials /Exams–**

The course had 6 tutorials some of which were challenging. The instructor also asked to hand in one tutorial. There was a programming assignment on Monte Carlo simulations and Kalman filtering.

The tests were as follows:

1) 3 quizzes : Fairly straightforward

2) The midsem and endsem exams were lengthy and a bit on the difficult side.

**Difficulty (on a scale of 1-5 with 5 being very tough) –**

4

**Textbooks**/**References**

Random Processes for Engineers by Bruce Hajek

**Reviewed by**

Bhishma Dedhia