Faedon / stats-110

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

Helpful Links

• MathJax Documentation
• LaTeX/Mathematics
• LaTeX Symbols
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