Wasserman

Notes and solutions from Larry Wasserman's All of Statistics.

Probability

• Introduction
• Sample Spaces and Events
• Probability
• Probability on Finite Sample Spaces
• Independent Events
• Conditional Probability
• Baye's Theorem

Random Variables

• Introduction
• Distribution and Probability Functions
• Some Important Discrete Random Variables
• Some Important Continuous Random Variables
• Bivariate Distributions
• Marginal Distributions
• Independent Random Variables
• Conditional Distributions
• Multivariate Distributions
• Two Important Multivariate Distributions
• Transformations of Random Variables
• Transformations of Several Random Variables

Expectation

• Expectation of a Random Variable
• Properties of Expectation
• Variance and Covariance
• Expectation and Variance of Important Random Variables
• Moment Generating Functions

Inequalities

• Probabiliy Inequalities
• Inequalities for Expectation

Convergence of Random Variables

• Introduction
• Types of Convergence
• The Law of Large Numbers
• The Central Limit Theorem
• The Delta Method

Models, Statistical Inference and Learning

• Parametric and Nonparametric Methods
• Fundamental Concepts in Inference

Estimating the CDF and Statistical Functionals

• The Empirical Distribution Function
• Statistical Functionals

The Boostrap

• Simulation
• Bootstrap Estimation of Variance
• Bootstrap Confidence Intervals

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