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Statistics 110

Notes, hand-drawn images, and a bit of Python code for Statistics 110: Probability course on iTunes, taught by Joe Blitzstein, Harvard University.

Intuitive Explanations

Download the Probability Cheatsheet

Requirements

Requires Python 3.5 or greater.

If you are seeing an annoying trailing line at the right for the embedded MathJax images, please see this Stack Overflow question IPython (Jupyter) notebook producing ghost line in all equations for an explanation and quick work-around solution.

Lectures

  1. Probability and Counting
  2. Story Proofs, Axioms of Probability
  3. Birthday Problem, Properties of Probability
  4. Conditional Probability
  5. Conditioning Continued, Law of Total Probability
  6. Monty Hall, Simpson's Paradox
  7. Gambler's Ruin and Random Variables
  8. Random Variables and Their Distributions
  9. Expectation, Indicator Random Variables, Linearity
  10. Expectation, Continued
  11. The Poisson Distribution
  12. Discrete vs. Continuous, the Uniform
  13. Standard Normal, Normal-normalizing constant
  14. Normal distribution, standardization, LOTUS
  15. Midterm review, skipping
  16. Exponential distribution, memorylessness property
  17. Moment Generating Functions (MGFs), hybrid Bayes' rule, Laplace's rule of succession
  18. MGFs to get moments of Expo and Normal, sums of Poissons, joint distributions
  19. Joint, conditional, and marginal distributions, 2-D LOTUS, expected distance between Uniforms, chicken-egg
  20. Expected distance between Normals, Multinomial, Cauchy
  21. Covariance, Correlation, Variance of a sum, Variance of Binomial & Hypergeometric
  22. Transformations, Log-Normal, Convolutions, Proving Existence
  23. Beta distribution, Bayes' Billiards
  24. Gamma distribution, Poisson processes
  25. Beta-Gamma, Order Statistics, Conditional Expection, 2-envelope Paradox
  26. 2-envelope paradox (cont.), Conditional Expectation (cont.), Waiting for HT vs. waiting for HH
  27. Conditional expectation (cont.); taking out what's known; Adam's Law, Eve's Law; projection picture
  28. Sum of a random number of random variables; inequalities (Cauchy-Schwarz, Jensen, Markov, Chebyshev)
  29. Law of Large Numbers, Central Limit Theorem
  30. Chi-Square, Student's t, Multivariate Normal
  31. Markov chains, Transition Matrix, Stationary Distribution
  32. Markov chains (cont.), irreducibility, recurrence, transience, reversibility, random walk on an undirected network
  33. Markov chains (cont.), Google PageRank as a Markov chain
  34. A Look Ahead; Examples of Regression Example, Sampling from a Finite Population

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  • Jupyter Notebook 100.0%