AI1110: Probability and Random Variables

1. Assessment

• Quizzes (best 3 out of 4): 30 marks
• Theory Assignment: 10 marks
• Programming Assignment: 10 marks
• Mid-Semester Examination: 20 marks
• End-Semester Examination: 30 marks
• Scribing (Additional): 5 marks

2. Instructor

• Name: Dr. Anjana A M
• Email: anjana.am@ee.iith.ac.in
• Office: EE-516, EECS Building
• Office Hours: Monday & Tuesday, 2:00–3:00 PM (with prior appointment)

3. Course TAs

MTech TAs:

BTech TAs:

• Boreddy Sri Sai Abhinav Reddy
• Gourishetty Himani
• Hari Krishna S
• Kotha Pratheek Reddy
• Kuruva Jeshwanth Krishna
• Pakala Tarun Reddy
• Pathri Vidya Praveen
• Tavva Dinesh Reddy
• Uppala Prajin
• Vallepu Preethika
Note: You are encouraged to email the TAs and discuss any doubts with them. However, please ensure that all communication remains respectful and professional. Abusive or inappropriate language will not be tolerated—humility and courtesy are expected at all times.

4. Class Timings

• Slot: D
• Timings:
  • Monday: 12:00 – 12:55
  • Tuesday: 09:00 – 09:55
  • Friday: 11:00 – 11:55
• Venue: LHC-LH14
• Online Platform: Google Classroom

5. Tutorial Timings

Saturdays 11:00 AM to 1:00 PM

6. Primary References

• Introduction to Probability, 2nd Edition, Athena Scientific, D. P. Bertsekas, J. N. Tsitsiklis
• A First Course in Probability, 10th Edition, Pearson, Sheldon. M. Ross
• Intuitive Probability and Random Processes with MATLAB, 1st Edition, Springer, Steven M. Kay.
• Probability with Engineering Applications, ECE313 Course Notes, University of Illinois, Urbana-Champaign, Bruce Hajek.
• Random Processes for Engineers, Bruce Hajek, Cambridge University Press, 2015. (Preproduction print available for free download here.)

7. Tentative List of Topics

• Course logistics and introduction to probability
• Preliminaries: set theory, functions, cardinality, countability, Permutations and combinations
• Axiomatic definition of probability: Motivation and paradoxes (Bertrand’s paradox)
• Discrete and continuous probability laws
• Conditional probability and independence: Total Proabability, Bayes' theroem
• Discrete random variables: PMF and CDF, Common distributions, Expectation and variance, Joint and marginal distributions, Functions of random variables
• Continuous random variables: PDF and CDF, Common distributions, Linear scaling and moments, Joint and marginal PDFs, Multivariate Gaussians
• Derived distributions: Convolution, Correlation and covariance, Conditional expectation and variance
• Transforms: Probability generating function (PGF), Characteristic function, Moment generating function (MGF)
• Concentration inequalities
• Convergence of random variables and limit theorems
• Introduction to statistical estimation
• Introduction to random processes

8. Course Notes from Jan-April 2025 Semester

Scribed course notes from jan-apr 2025 can be found here.

9. Academic Honesty and Plagiarism

Students are encouraged to discuss class materials and assignments with peers. However, verbatim copying from friends, books, or online sources in exams and assignments — including programming assignments — is strictly prohibited. Collaboration in understanding and solving assignments is acceptable, but all solutions and code must be written independently. Any instance of copying in assignments or exams will result in a fail grade. See this page (maintained by the CSE department), this page, and this one to understand more about plagiarism.