Probability for Statistics and Machine Learning

Front Matter Pages i-xix

Book Chapter Pages 1-93

Review of Univariate Probability


Book Chapter Pages 95-121

Multivariate Discrete Distributions


Book Chapter Pages 123-165

Multidimensional Densities


Book Chapter Pages 167-197

Advanced Distribution Theory


Book Chapter Pages 199-219

Multivariate Normal and Related Distributions


Book Chapter Pages 221-248

Finite Sample Theory of Order Statistics and Extremes


Book Chapter Pages 249-292

Essential Asymptotics and Applications


Book Chapter Pages 293-322

Characteristic Functions and Applications


Book Chapter Pages 323-338

Asymptotics of Extremes and Order Statistics


Book Chapter Pages 339-374

Markov Chains and Applications


Book Chapter Pages 375-400

Random Walks


Book Chapter Pages 401-436

Brownian Motion and Gaussian Processes


Book Chapter Pages 437-462

Poisson Processes and Applications


Book Chapter Pages 463-504

Discrete Time Martingales and Concentration Inequalities


Book Chapter Pages 505-526

Probability Metrics


Book Chapter Pages 527-558

Empirical Processes and VC Theory


Book Chapter Pages 559-582

Large Deviations


Book Chapter Pages 583-612

The Exponential Family and Statistical Applications


Book Chapter Pages 613-687

Simulation and Markov Chain Monte Carlo


Book Chapter Pages 689-746

Useful Tools for Statistics and Machine Learning


Back Matter