### EE 325 – PROBABILITY AND RANDOM PROCESSES

**Course offered in:**

Spring 2013

**Professor**

Prof. Sibi Raj Pillai

**Course Content**

- Classical Probability
- Bertrand’s paradox
- Axiomatic Probability
- Constructing Probability Spaces (Basic Measure Theory)
- Borel Fields
- Discrete and Continuous Random Variables
- Conditionality and Independence
- Distributions
- Generating functions
- Markov Chains
- Gaussian Random Vectors
- Characteristic Functions
- Detection Theory

**Pre requisites**

Basic Probability, Mathematical Maturity, IC 102(Not in strict sense though)

**Feedback on lectures**

Lectures were very good. Professor was patient enough to explain certain topics several times if needed. Notes were put up on his homepage(link given below) but were sometimes delayed.

**Feedback on tutorials, assignments and exams**

There were 7 tutorials and 3 home works. All were somewhat difficult and needed efforts/ideas. Tutorials were discussed in class (At least, motivation to problems was explained). We were needed to submit tutorial solutions (for no marks). Additionally, two large sets of worked out problems were also given. Exams had NO theory and problems were more or less tweaked versions of the tough questions asked in tutorials/homeworks/solved problems making slightly more tougher. 3 quizzes, a midsem and an endsem were conducted with the weightage of quiz 1 reduced due to poor performance.

**Difficulty level**

Difficult.

**Grading**

Something to worry about. 25 FRs in 2012-13 and 16 in 2013-14. CC and DD were of high concentration in 2012-13 and BC and CC during 2013-14. The other grades had around 10-15 members.

**Study Material and References**

Comprehensive notes/materials were put up on the his homepage. Notes covered entire theory but not many examples. Writing down at least examples in class will help a lot.

**Link to lectures**

http://www.ee.iitb.ac.in/~bsraj/courses/ee325/

**Text**

Probablity,Random variables and Stochastic Processes by Athanasious Papoulis and S.UnniKrishna Pillai.

**Miscellaneous**

Many students badly faltered in Quiz 1 and midsem as questions seemed inordinately difficult while most of them were actually on the lines of tutorials. Post midsem, many students took tutorials seriously and the performance increased remarkably.

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

EE 601-Statistical Signal Analysis

EE 621-Markov Chains and Queuing systems

EE 703-Digital Message Transmission

EE 734-Advanced Probability and Random Processes for Engineers

EE 736-Introduction to Stochastic Optimization

EE 737-Introduction to Stochastic Control

CS 419- Introduction to Machine Learning

CS 726-Advanced Machine Learning

CS 729-Topics in Machine Learning

IE 708-Markov Decision Processes

**Application of course in other courses and practice**

- Course is a hard prerequisite to many CSP courses.
- Finds several application in EE 308(Communication Systems), and Detection theory forms the backbone of EE 328(Digital Communications).
- Noise in transmission of signals is modelled using known probability distributions/Random Variables(typically Gaussian).
- All Machine Learning courses rely entirely on Probability. Speech/Image Recognition softwares use Markov Chains extensively.

Review written by Tharun Kumar Reddy(tharunkumarreddy24@gmail.com)