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.
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
- Probability and Counting
- Story Proofs, Axioms of Probability
- Birthday Problem, Properties of Probability
- Conditional Probability
- Conditioning Continued, Law of Total Probability
- Monty Hall, Simpson's Paradox
- Gambler's Ruin and Random Variables
- Random Variables and Their Distributions
- Expectation, Indicator Random Variables, Linearity
- Expectation, Continued
- The Poisson Distribution
- Discrete vs. Continuous, the Uniform
- Standard Normal, Normal-normalizing constant
- Normal distribution, standardization, LOTUS
- Midterm review, skipping
- Exponential distribution, memorylessness property
- Moment Generating Functions (MGFs), hybrid Bayes' rule, Laplace's rule of succession
- MGFs to get moments of Expo and Normal, sums of Poissons, joint distributions
- Joint, conditional, and marginal distributions, 2-D LOTUS, expected distance between Uniforms, chicken-egg
- Expected distance between Normals, Multinomial, Cauchy
- Covariance, Correlation, Variance of a sum, Variance of Binomial & Hypergeometric
- Transformations, Log-Normal, Convolutions, Proving Existence
- Beta distribution, Bayes' Billiards
- Gamma distribution, Poisson processes
- Beta-Gamma, Order Statistics, Conditional Expection, 2-envelope Paradox
- 2-envelope paradox (cont.), Conditional Expectation (cont.), Waiting for HT vs. waiting for HH
- Conditional expectation (cont.); taking out what's known; Adam's Law, Eve's Law; projection picture
- Sum of a random number of random variables; inequalities (Cauchy-Schwarz, Jensen, Markov, Chebyshev)
- Law of Large Numbers, Central Limit Theorem
- Chi-Square, Student's t, Multivariate Normal
- Markov chains, Transition Matrix, Stationary Distribution
- Markov chains (cont.), irreducibility, recurrence, transience, reversibility, random walk on an undirected network
- Markov chains (cont.), Google PageRank as a Markov chain
- A Look Ahead; Examples of Regression Example, Sampling from a Finite Population
Helpful Links
- MathJax Documentation
- LaTeX/Mathematics
- LaTeX Symbols
- Can't remember that
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