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The Theory of Probability

Explorations and Applications

Santosh S. Venkatesh

About the book

From its classical foundations to the advanced modern theory, a self-contained guide to probability that weaves together proofs, historical context, and detailed applications. The plan was a week per chapter through Part A.

Prerequisites

A foundation in mathematical analysis and linear algebra is recommended.

Sessions

26 of 27 sessions were recorded. Dates are IST.

  1. 9 Sep Probability Spaces (Part 1) provisional Introduction to probability spaces and basic concepts ▶ 58 min
  2. 10 Sep Probability Spaces (Part 2) provisional Sigma-algebras and measurable spaces ▶ 1 h 11 min
  3. 11 Sep Probability Spaces (Part 3) provisional Probability measures and their properties ▶ 1 h 12 min
  4. 12 Sep Probability Spaces (Part 4) provisional Random variables and distributions ▶ 1 h 14 min
  5. 13 Sep Probability Spaces (Part 5) provisional Expectation and moments ▶ 41 min
  6. 15 Sep Session 6 provisional ▶ 53 min
  7. 16 Sep Conditional Probability (Part 1) provisional Basic concepts of conditional probability ▶ 58 min
  8. 17 Sep Conditional Probability (Part 2) provisional Bayes' theorem and its applications ▶ 1 h 23 min
  9. 18 Sep Conditional Probability (Part 3) provisional Conditional expectation ▶ 1 h 01 min
  10. 22 Sep Session 10 provisional ▶ 1 h 05 min
  11. 23 Sep A First Look at Independence (Part 1) provisional Introduction to independence ▶ 1 h 05 min
  12. 24 Sep A First Look at Independence (Part 2) provisional Product measures and independent events ▶ 47 min
  13. 26 Sep A First Look at Independence (Part 4) provisional Sums of independent random variables ▶ 1 h 07 min
  14. 27 Sep A First Look at Independence (Part 5) provisional The law of large numbers ▶ 38 min
  15. 29 Sep Session 15 provisional ▶ 1 h 04 min
  16. 1 Oct Probability Sieves (Part 2) provisional Inclusion-exclusion principle ▶ 50 min
  17. 2 Oct Probability Sieves (Part 3) provisional Erdős–Ko–Rado theorem ▶ 58 min
  18. 3 Oct Probability Sieves (Part 4) provisional Sieve of Eratosthenes probabilistic version ▶ 1 h 04 min
  19. 4 Oct Probability Sieves (Part 5) provisional Large sieve inequality ▶ 1 h 18 min
  20. 14 Oct The Normal Law (Part 1) provisional Introduction to the normal distribution ▶ 43 min
  21. 15 Oct The Normal Law (Part 2) provisional Properties of the normal distribution ▶ 1 h 03 min
  22. 17 Oct The Normal Law (Part 4) provisional Proofs of the CLT ▶ 39 min
  23. 22 Oct Probabilities on the Real Line (Part 2) provisional Lebesgue-Stieltjes measures ▶ 54 min
  24. 23 Oct Probabilities on the Real Line (Part 3) provisional Convolutions and characteristic functions ▶ 59 min
  25. 25 Oct Probabilities on the Real Line (Part 5) provisional Stable distributions ▶ 47 min
  26. 27 Oct Session 26 provisional ▶ 37 min