Probability for statistics and machine learning: fundamentals and advanced topics/ Anirban DasGupta

Includes index

Review of univariate probability -- Multivariate discrete distributions -- Multidimensional densities -- Advanced distribution theory -- Multivariate normal and related distributions -- Finite sample theory of order statistics and extremes -- Essential asymptotics and applications -- Characteristic functions and applications -- Asymptotic of extremes and order statistics -- Markov chains and applications -- random walks -- Brownian motion and Gaussian processes -- Poisson processes and applications -- Discrete time martingales and concentration inequalities -- Probability metrics -- Emperical processes and V C theory -- Large deviations -- The exponential family and statistical applications -- Simulation and Markov chain Monte Carlo -- Useful tools for statistics and machine learning