• Modified the wording and hint of Exercise 18 in the Random walk page.

• Added hint to Exercise 31 in the Distributions with finite supports page.

• Also corrected a minor typo in the same page pointed out by Avigyan.

• Updated the hints to Exercise 25 in the Distributions with infinite supports page. Thanks to Souradip for pointing out the need.

• Updated the hints to Exercises 25 and 26 in the Distributions with finite supports page. Thanks to Mayukh for pointing out the need.

• Added Souradip’s mysterious simplification of the solution to Exercise 35 in the Conditional distribution page.

• Corrected a copy-paste error in the finite and infinite supports pages. Thanks to Arshia for pointing out the error.

• More minor typos fixed here and there.

• More hints added.

• Added Samyak’s brilliant solution of Exercise 17(c) to the
  Conditional distribution page.

• More hints added.

• Added some extra discussion to the existing hint of Exercise 25 in the Conditional distribution page.

• Added hint to Exercise 22 of the Distributions with finite supports page.

• Added hints to more problems.

• Added hints to more problems.

• Simplified the hint of Exercise 11 in the Random Walk page.

• Added hints to all the conditional distribution problems.

• Also added a last exercise in the joint distributions page.

• Corrected minor typos here and there. Thanks to Tushti and Mayukh.

• Slightly reworded the definition of memorylessness. Now it referes to only nonnegative random variables. The change, though minor to look at, is important. Earlier I was allowing X to be negative also (by mistake), so Geometric was not memoryless according to that wrong definition!

• Added videos to the PGF page.

• Finished classifying all the exercises as Easy, Medium or Hard.

• Classified most of the exercises as Easy, Medium or Hard. The classification is not yet complete.

• Added video links to the Random walk page.

• Corrected hint to Exercise 9 in the Conditional distribution page.

• Added a detailed hint to Exercise 7 (the most important result) in the PGF page.

• Corrected a serious mistake in the hint of Exercise 16 in the Conditional distribution page. Thanks to Nuhad.

• Added some AI-generated interactive simulation of the capture-recapture method. See it here. It is also linked from the Distributions with finite supports page. The code is completely written by ChatGPT.

• Made the hint of Exercise 25 more lucid in the Conditional distribution page.

• Made the hint of Exercise 18 more lucid (hopefully!) in the Conditional distribution page.

• Slightly reworded the tower property and its proof. Also corrected a minor typo in the solution of Example 2 in the Conditional distribution page. Thanks to Ankush and Arindrajit.

• Corrected a typo in the answer of Exercise 7 in the Distributions with finite supports page. Thanks to Mayukh.

• Corrected a typo in the answers of Exercises 6, 11 and 12 in the Distributions with infinite supports page. Thanks to Mayukh.

• Corrected a typo in the hint of Exercise 2 in the Conditional distribution page. Thanks to Samyak.

• Corrected a typo in the proof of Cauchy-Schwarz inequality in the Joint distribution page. Thanks to Nuhad.

• Corrected a typo in the hint of Exercise 21 in the Joint distribution page. Thanks to Nuhad.

Corrected some silly typos in the solution of Exercise 6 in the Conditional distribution page. Thanks to Tanmay Rai.

• Corrected a serious typo in the two important exercises added yesterday in the Conditional distribution page.

  • Updated the Random walk page.

• Corrected a few typos in the Infinite support page. Thanks to Mayukh.

Added two important exercises in the Conditional distribution page.

Corrected a typo in the hint of Exercise 21 in the Joint distribution page.

Added a picture to the Joint distribution page.

• Added a couple of warnings to the
  Expectation page.

• Improved the presentation in the Joint distribution page.

• Added proof of a theorem regarding expectation of max in the Expectation page.

• Also added an example (Example 1) of a random variable with undefined expectation in the same page. The example is thanks to Bodhisatva.

• Corrected a mistake in the solution to Exercise 35 in the Basic concepts page. Thanks to Titeer.

• Added a smart solution to Exercise 28 in the Expectation page.

• Corrected a mistake in the solution of Exercise 29 in the Basic concepts page. Thanks to Nipam.
• Corrected a typo in the solution of Exercise 13 in the Random variables page. Thanks to Avigyan.

• Corrected a typo in the statement of Bayes theorem (version 2). Also the answer to Exercise 36 in the same page. Thanks to Avigyan.
• Corrected a typo in the hint for Exercise 4 in the Random variables page. Thanks to “Chaitu”.

• Added hints to all the exercises in the Random variables page.

• Corrected a serious mistake in the hint of Exercise 32 in the basic concepts page. Thanks to Sayantan.

• Corrected a mistake in the solution of Exercise 23 in the Expectation page. Thanks to Nipam.
• Corrected some typos in the basic concepts page. Thanks to Sayantan.
• Corrected a serious mistake in the solution of Exercise 31 in the conditional probabilty page. Thanks to Titas.

Added a video providing complete discussion of Exercise 42 in the conditional probabilty page. This is the Ace of Spades problem asked by Nipam.

Corrected the answer to Exercise 13 in the conditional probabilty page. Thanks to Anant Raj.

• Blank hints filled in the conditional probabilty page.
• Slightly simplified the discussion in the random variables page.

Corrected the hint to Exercise 31 in the conditional probabilty page. Thanks to Roshan.

Corrected the hint to Exercise 49 in the conditional probabilty page. Thanks to Rishit Garg.

Removed an exercise (it was Exercise 8) from the conditional probabilty page. It has been moved to a topic near the end of the course.

Correction to the solution of exercise 19 in the basic concepts page suggested by the students.

Correction to the solution of exercise 14 in the basic concepts page suggested by the students.

• Added an example and two exercises to the Independence page.
• Introduced the concept of box events in the same page.

• Added the very elegant solution discussed in class to exercise 24 in the basic concepts page. Also corrected the earlier solution.
• Added a hint to the last problem in the Independence page.

• Animation added for branching processes.
• Exercises added for PGF in the same page.