6.431x Probability - The Science of Uncertainty and Data

General

• Seeing Theory by Daniel Kunin - "a visual introduction to probability and statistics"
  • (especially) Discrete and Continuous section for visualizing common distributions

Unit 1: Probability models and axioms

Lec. 1: Probability models and axioms

Mathematical background: Sets; sequences, limits, and series; (un)countable sets

Unit 2: Conditioning and independence

Lec. 2: Conditioning and Bayes' rule

• Bayes theorem by 3Blue1Brown
• Bayes' theorem calculator by Richard Lowry

Lec. 3: Independence

Unit 3: Counting

Lec. 4: Counting

Unit 4: Discrete random variables

Lec. 5: Probability mass functions and expectations

Lec. 6: Variance; Conditioning on an event; Multiple r.v.'s

Lec. 7: Conditioning on a random variable; Independence of r.v.'s

Unit 5: Continuous random variables

Lec. 8: Probability density functions

• Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2 by 3Blue1Brown

Lec. 9: Conditioning on an event; Multiple r.v.'s

• Joint Distributions, Independence by Jeremy Orloff and Jonathan Bloom

Lec. 10: Conditioning on a random variable; Independence; Bayes' rule

• Conditional Probability given Joint PDF by Michelle Lesh

Unit 6: Further topics on random variables

Lec. 11: Derived distributions

Lec. 12: Sums of independent r.v.'s; Covariance and correlation

Lec. 13: Conditional expectation and variance revisited; Sum of a random number of independent r.v.'s

• Conditional expectations, discrete random variables by Jochumzen
• Conditional expectations, continuous random variables by Jochumzen

Unit 7: Bayesian inference

Lec. 14: Introduction to Bayesian inference

• Bayesian Inference (Probability Course) by Hossein Pishro-Nik
• Binomial distributions | Probabilities of probabilities, part 1 by 3Blue1Brown
• Bayesian Updating: Continuous Priors by MIT OCW (18.05 Spring 2014)
• A Student's Guide to Bayesian Statistics by Ben Lambert
• inferring the bias of a coin with bayes / beta by joost2076

Lec. 15: Linear models with normal noise

Lec. 16: Least mean squares (LMS) estimation

Lec. 17: Linear least mean squares (LLMS) estimation

Unit 8: Limit theorems and classical statistics

Lec. 18: Inequalities, convergence, and the Weak Law of Large Numbers

Lec. 19: The Central Limit Theorem (CLT)

Lec. 20: An introduction to classical statistics

Unit 9: Bernoulli and Poisson processes

Lec. 21: The Bernoulli process

Lec. 22: The Poisson process

Lec. 23: More on the Poisson process

Unit 10: Markov chains

Lec. 24: Finite-state Markov chains

Lec. 25: Steady-state behavior of Markov chains

Lec. 26: Absorption probabilities and expected time to absorption