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Last updated on: Sun Aug 02 11:11:52 IST 2026


1. Probability II (BSDS 2nd year, 2026)

URL: https://arnabc74.github.io/BSDSprob2_2026/
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1.1. Class notes

  1. Motivation behind probability
  2. Transformation of random vectors using Jacobian
  3. Expectation and variance of random vectors
  4. Sampling distributions of normal mean and variance
  5. Probability generating function (PGF)
  6. Some inequalities
  7. Borel-Cantelli lemmas
  8. Convergence of random variables
  9. Convergence of expectations
  10. Miscellaneous tools
  11. Characteristic function (CF)

1.2. Projects

Each of the following project is a group project to be done by around 5 students each. Each project will be done by multiple groups. Each group does one project. Exact logistics will be communicated later.
  1. Box-Muller transform and other related simulation techniques
  2. Face recognition using eigenanalysis (computational aspect, moderate).
  3. Count-min sketch to approximate frequencies from an input stream.
  4. BJKST algorithm for counting distinct elements from an input stream.
  5. Showing almost every number is a normal number.
  6. Showing that a random walk in 3D may not return.
These are more like elaborate assignments than projects demanding original research. You are welcome to discuss the projects among yourselves. All the projects will be introduced during the lectures at appropriate time points.

1.3. Instructor and TAs

Instructor: Arnab Chakraborty (arnabc74 at gmail)

TA for Kolkata: Debanjan Bhattacharjee (debanjanbhattacharjee2002 at gmail)

TA for Delhi: Sumangal Bhattacharya (sumangalbisi82 at gmail)

TA for Bangalore: Sayan Roy (rs_math2404 at isibang)

1.4. Marks distribution

1.5. References

The class notes constitute the main reference. It is based on many sources including the following books: Unfortunately, to my knowledge, there is no textbook just suitable for this course. The first two books mentioned above are the closest from the easier side. They, however, do not mention many of the advanced topics included in our syllabus. The last two books do mention them, but contain way too much discussion and are written at a level much higher than the present course.

In short: the class notes are your best reference!