Problems in Probability

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Quick Concepts

Sampling Table and Multiplication Rule
Some Story Proofs
Factorial Approximations
Definitions of Probability
Inclusion-Exclusion Principle
Bayes' Rule and Law of Total Probability
Odds Form of Bayes' Rule
Random Variables Intro
Simpson's Paradox
Gambler's Ruin and First-Step Analysis
Linearity and Fundamental Bridge
Bernoulli Distribution
Binomial Distribution
Geometric and "First-Success" Distributions
Negative Binomial Distribution
Hypergeometric Distribution
Poisson Distribution
Normal Distribution
Uniform Distribution and Universality of the Uniform
Exponential Distribution
Gamma Distribution
Beta Distribution
Chi-Squared Distribution
Student-t Distribution
Cauchy Distribution
Multinomial Distribution
Multivariate Normal Distribution
Uniform on a Region
Connections Between Distributions
Moment-Generating Functions
Order Statistics
"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
Statistical Inequalities
Markov Chains
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."
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