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Probability Theory and Statistics Lecture notes
The aim of the notes is to combine the mathematical and theoretical underpinning of statistics and statistical data analysis with computational methodology and practical applications. Topics covered includes: Notion of probabilities, Probability Theory, Statistical models and inference, Mean and Variance, Sets, Combinatorics, Limits and infinite sums, Integration.
Author(s): Niels Richard Hansen
294 Pages 
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
Lecture Notes on Free Probability Theory
to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. This note contains below topics, Very Short Introduction into Subject and History, The Notion of Freeness Definition Example and Basic Properties, Emergence of the Combinatorics of Free Probability Theory Free Central Limit Theorem, The Combinatorics of Free Probability Theory Free Cumulants, Free Convolution of Compactly Supported Probability Measures and the RTransform, Free Convolution of Arbitrary Probability Measures and the Subordination Function, Gaussian Random Matrices and Asymptotic Freeness, Unitary Random Matrices and Asymptotic Freeness and a Remark on Wigner Matrices, Von Neumann Algebras The Free Group Factors and Relation to Freeness, Circular and RDiagonal Operators, Applications of Freeness to von Neumann Algebras Compression of Free Group Factors, Some More Operator Algebraic Applications of Free Probability.
Author(s): Roland Speicher
119 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
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