Table of Distributions
Sampling Table and Multiplication Rule
Some Story Proofs
Definitions of Probability
Bayes' Rule and Law of Total Probability
Odds Form of Bayes' Rule
Random Variables Intro
Gambler's Ruin and First-Step Analysis
Linearity and Fundamental Bridge
Geometric and "First-Success" Distributions
Negative Binomial Distribution
Uniform Distribution and Universality of the Uniform
Multivariate Normal Distribution
Uniform on a Region
Connections Between Distributions
"Law of the Unconscious Statistician"
Covariance and Correlation
Transformations and Jacobians
Joint, Marginal, and Conditional Distributions
Conditional Expectation and Conditional Variance
Central Limit Theorem and Law of Large Numbers
"Mathematics is the logic of certainty, but
statistics is the logic of uncertainty."
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