### IE 502 – PROBABILISTIC MODELS

**Course offered in:**

Spring 2019

**Instructors:**

Prof. K.S. Mallikarjuna Rao

**Prerequisites:**
There were no hard prerequisites for this course, however, a sound knowledge of the concepts of Probability discussed in high school will come really handy.

**Course Content:**

- Probability, Conditioning and Independence
- Random Variables, Limit Theorems, Random Walks
- Markov chains, Martingales, Poisson processes, Renewal processes, Queuing and Reliability, and Applications. (This topic was discussed on an elementary level, it is taken up in detail in the course IE 611, hence this course i.e. IE 502 serves as a prerequisite for IE 611)

**Feedback on Lectures:**

The Professor used slides for reference in the lectures. He also explained the important topics, solved examples, and brief proofs of some of the theorems on board. The slides used initially were quite detailed but the latter ones lacked content and can only be used to just quickly go through the main topics covered in lectures and not all of what was discussed. The Professor didn’t care much about the attendance and there was no contribution of attendance to the evaluation of grades. But, you were required to attend the lectures and take proper notes, as the professor released the notes and lecture slides a day before the exam or quiz, and the content was not detailed enough. The course material put up on Moodle was not self-explanatory and would make sense to you only if you have been regular in the lectures.

The course content wasn’t very rigorous and a little effort from your end will be sufficient. You might find yourself a bit uncomfortable with some of the notations introduced in this course, but practicing questions dealing with these notations will help you understand them better. The last portion of this course including Markov chains, queuing theory, etc. will be a bit on the tougher side when compared against the other content of this course. But, the professor will deal with only the elementary concepts, and reading the relevant part from any of the reference books will help you in understanding it better.

**Feedback on Tutorials, Assignments and Exams:**
Not too many tutorials were released for this course, only once before every quiz or mid-sem/endsem. The tutorials were not graded, but doing them sincerely helped a lot as the questions in the quizzes/mid-sems/end-sems were a lot similar to the ones they gave in tutorials. The tutorial discussions were scheduled in the lectures itself, and there were no separate slots for it. Prior information regarding the tutorial-discussion lectures was released and the TAs used to take these lectures cum tutorial discussions.

The exams consisted of questions ranging between easy to moderate difficulty level. There were many instances when questions were directly asked from one of the reference books, especially in quizzes. Being regular with lectures and listening attentively to them, attempting the tutorials and getting your doubts cleared in the discussion sessions, and referring the textbook for any of the concepts you are not very clear with will help you easily score a great grade in this course.

**Difficulty:**

(on a scale of 1 being very easy to 5 being very hard): 2

**Study Material and References:**

These were the references suggested by the Professor for the course.

- Dimitri P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, Athena Scientific.
- Kai L. Chung, A Course in Probability Theory, Academic Press.
- William Feller, An Introduction to Probability Theory and Its Applications (2 Vols), Wiley.
- Charles M. Grinstead and J. L. Snell, Introduction to Probability, AMS.
- Jim Pitman, Probability, Springer.
- Jean Jacod and Philip Protter, Probability Essentials, Springer.
- Sheldon Ross, Probability Models, Academic Press.
- Santosh S. Venkatesh, The Theory of Probability, Cambridge University Press.

I personally referred to the textbook by Sheldon Ross. It was easy to follow and the questions served as nice practice problems.

**Grading Statistics:**
AA 4
AB 30
AU 1
BB 39
BC 22
CC 14
PP 33
S 12
W 7
Total 162

**Additional comments & what you learnt from the course:**
This course is one of the fundamental courses for IEOR minor program and thus serves as a pre-requisite for many advanced courses in the minor program. Although, the Department of Electrical Engineering itself has a few core courses on probability and statistics, and you can use their background to take up these advanced courses, but, it entirely depends on the discretion of the instructor of the course you intend to take up. So, it’s not a bad idea to finish off this course.
Also, it introduces you with concepts like Markov chains, Queuing theory which are generally not taken up in electrical core courses on Probability. Although, due to the pandemic the instructor was not able to cover this topic and hence released reading material on Moodle for the completion of these topics and the course itself.
Review by – Anjali Yadav
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