Course Review IE 621

IE 621 - Introduction to Probability and Stochastic Processes I

Year: 2023-24 Autumn Semester
Instructor: Prof. K S Mallikarjuna Rao

Motivation

Embarking on IE 621 - Introduction to Probability and Stochastic Processes I lays the foundation for a profound exploration of uncertainty and randomness. In the intricate realm of machine learning, probability and stochastic processes serve as indispensable tools for modeling and understanding complex systems. This course opens doors to a world where uncertainties are not roadblocks but opportunities for insightful analysis and prediction.

Course Content

The official course content can be found here. The updated syllabus is listed below:

• Introduction to Probability: conditional probability, independence, discrete random variables, expectation, moments, random vectors, joint and marginal distributions, continuous random variables, expectation, moments, joint and marginal densities, laws of large numbers, inequalities in probability.
• Elementary stochastic processes: random walks, Markov chains: first step analysis, state classifications, invariant distributions, Finite state Markov chains, Chapman-Kolmogorov equations, limiting state probabilities, Stationary distributions.
• Counting processes. Poisson process. Memory-less property of exponential random variables and related models & examples. Basics of queuing theory, renewal theory, and applications.

Feedback on Lectures

• Teaching Style: The lectures delivered by the instructor were unequivocally disappointing, making the course an exceptionally challenging experience. Profoundly lacking in teaching competence, the instructor exhibited a dismal ability to communicate complex concepts, leaving students bewildered and frustrated. The lectures were characterized by an utter lack of clarity, coherence, and organization, as Prof. Rao failed to provide a structured learning experience. Moreover, there was a blatant disregard for student understanding, exemplified by the instructor’s unwillingness to address queries or provide adequate explanations. Overall, this course, under the instruction of Prof. Rao, stands out as one of the worst experiences in the academic journey at IIT Bombay.
• Attendence: Mandatory to attend 80% of the lectures.

Feedback on Assignments and Exams

• Weightage: Quizzes - 30%, Midsem - 30%, Endsem - 40%
• Pattern: The exams administered were an egregious display of incompetence, reflecting a complete disregard for fair assessment. The questions predominantly revolved around modeling, swinging between unnecessarily complex and overly simplistic, creating an arbitrary and inconsistent difficulty level. The presence of incorrect questions, unclear problem statements, and occasional omission of crucial data further compounded the overall chaos. Shockingly, modeling of Markov chain, proofs were demanded, an aspect not adequately covered in class, leaving students grappling with unfamiliar territory. To add insult to injury, the exams ventured into the absurd realm of asking questions directly from research papers, showcasing a severe disconnect between the exam content and the course material. This blatant mishandling of assessments only served to deepen the dissatisfaction and frustration among students.

Difficulty Level

The difficulty level of the course was undeniably on the negative end, leaning towards the moderately difficult spectrum. The course content, particularly focused on topics like Markov Chains, Poisson Processes, and Renewal Processes, proved to be difficult as it demands modeling type questions in exam. The questions, especially those concerning these specific concepts, were exceptionally tough, pushing students beyond their limits. Compounding the challenge, the lackluster teaching by the instructor intensified the difficulty, necessitating an enormous amount of hard work and efforts from students to compensate for the instructional shortcomings. Consequently, the course demanded an exorbitant amount of time investment, far exceeding what is reasonable for a course of this nature.

Prerequisites

While there are no formal prerequisites for IE 621, prospective students are strongly advised to possess a solid foundation in fundamental probability concepts. A comprehensive understanding of basic probability theory, including events, random variables, and probability distributions, will significantly ease the learning curve. Proficiency in mathematical concepts such as calculus and algebra is essential, as these skills serve as the backbone for tackling the advanced topics covered in the course.

Grading Stats

Reference Books

• Athanasios Papoulis, S. Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes
• Sheldon M. Ross, Introduction to Probability Models

Reviewed by

Soumen Mondal (Email: 23m2157@iitb.ac.in)