Generalized Probability Theory notes for a short course

Introduction to Probability

This book contains below topics, Discrete Probability Distributions, Continuous Probability Densities, Combinatorics, Conditional Probability, Distributions and Densities, Expected Value and Variance, Sums of Random Variables, Law of Large Numbers, Central Limit Theorem, Generating Functions, Markov Chains, Random Walks.

Author(s): Charles M. Grinstead and J. Laurie Snell

518 Pages

Lecture Notes on Free Probability

This note contains below topics, Noncommutative probability spaces and distributions, Free Cumulants, Additive free convolution and limit theorems, Asymptotic Freeness, Stransform, Subordination, Operatorvalued noncommutative random variables, Rdiagonal variables, Distributions of SelfAdjoint Variables and Their Transforms, Scaling Properties.

Author(s): Vladislav Kargin

148 Pages

Generalized Probability Theory notes for a short course

These notes treat quantum theory as a nonclassical probability calculus. They come from a short course on generalized probability theories. The idea goes back to von Neumann and to the later literature on quantum logics.

Author(s): Alex Wilce

75 Pages

Probability Theory and Examples

This note covers measure theory, Laws of large numbers, Central limit theorem, Martingales, Markov chains, Ergodic theorems, Brownian motion, Applications to random walk, Multidimensional Brownian motion.

Author(s): Rick Durrett

490 Pages

Basic probability theory

This note explains the following topics, events and probabilities, Combining events, Conditional probabilities, independence and bayes rule, Random variables and discrete distributions, Expectation and variance, Continuous random variables.

Author(s): Sharon Goldwater, University of Edinburgh

34 Pages

Probability Theory Lecture Notes by Phanuel Mariano

The contents include, Combinatorics, Axioms of Probability, Independence, Conditional Probability and Independence, Random Variables, Some Discrete Distributions, Continuous Random Variable, Normal Distributions, Normal approximations to the binomial, Some continuous distributions, Multivariate distributions, Expectations, Moment generating functions, Limit Laws.

Author(s): Phanuel Mariano

98 Pages

Lecture Notes for Introductory Probability

The contents include, Combinatorics, Axioms of Probability, Conditional Probability and Independence, Discrete Random Variables, Continuous Random Variables, Joint Distributions and Independence, More on Expectation and Limit Theorems, Convergence in probability, Moment generating functions, Computing probabilities and expectations by conditioning, Markov Chains, Introduction, Markov Chains, Classification of States, Branching processes, Markov Chains, Limiting Probabilities, Markov Chains, Reversibility, Three Application, Poisson Process.

Author(s): Janko Gravner, Mathematics Department, University of California

218 Pages

Lecture Notes Probability Theory

This book explains the following topics, Probability spaces, Random variables, Independence, Expectation, Convergence of sequences of random variables.

Author(s): Manuel Cabral Morais

275 Pages