Session 4 of 26 · 12 Sep 2025 · 1 h 14 min

Probability Spaces (Part 4)

Random variables and distributions

Notes for this session are on their way: they are being written from the transcript of the recording.

The Theory of Probability

5 Sep Introduction Session Welcome and overview of the book and reading group format not recorded
9 Sep Probability Spaces (Part 1) Introduction to probability spaces and basic concepts ▶ 58 min
10 Sep Probability Spaces (Part 2) Sigma-algebras and measurable spaces ▶ 1 h 11 min
11 Sep Probability Spaces (Part 3) Probability measures and their properties ▶ 1 h 12 min
12 Sep Probability Spaces (Part 4) Random variables and distributions ▶ 1 h 14 min
13 Sep Probability Spaces (Part 5) Expectation and moments ▶ 41 min
15 Sep Session 6 ▶ 53 min
16 Sep Conditional Probability (Part 1) Basic concepts of conditional probability ▶ 58 min
17 Sep Conditional Probability (Part 2) Bayes' theorem and its applications ▶ 1 h 23 min
18 Sep Conditional Probability (Part 3) Conditional expectation ▶ 1 h 01 min
22 Sep Session 10 ▶ 1 h 05 min
23 Sep A First Look at Independence (Part 1) Introduction to independence ▶ 1 h 05 min
24 Sep A First Look at Independence (Part 2) Product measures and independent events ▶ 47 min
26 Sep A First Look at Independence (Part 4) Sums of independent random variables ▶ 1 h 07 min
27 Sep A First Look at Independence (Part 5) The law of large numbers ▶ 38 min
29 Sep Session 15 ▶ 1 h 04 min
1 Oct Probability Sieves (Part 2) Inclusion-exclusion principle ▶ 50 min
2 Oct Probability Sieves (Part 3) Erdős–Ko–Rado theorem ▶ 58 min
3 Oct Probability Sieves (Part 4) Sieve of Eratosthenes probabilistic version ▶ 1 h 04 min
4 Oct Probability Sieves (Part 5) Large sieve inequality ▶ 1 h 18 min
14 Oct The Normal Law (Part 1) Introduction to the normal distribution ▶ 43 min
15 Oct The Normal Law (Part 2) Properties of the normal distribution ▶ 1 h 03 min
17 Oct The Normal Law (Part 4) Proofs of the CLT ▶ 39 min
22 Oct Probabilities on the Real Line (Part 2) Lebesgue-Stieltjes measures ▶ 54 min
23 Oct Probabilities on the Real Line (Part 3) Convolutions and characteristic functions ▶ 59 min
25 Oct Probabilities on the Real Line (Part 5) Stable distributions ▶ 47 min
27 Oct Session 26 ▶ 37 min