Probability, Random Processes, and Ergodic Properties

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

Introduction to Probability Theory and Statistics

This note covers the following topics: Probability, Random variables, Random Vectors, Expected Values, The precision of the arithmetic mean, Introduction to Statistical Hypothesis Testing, Introduction to Classic Statistical Tests, Intro to Experimental Design, Experiments with 2 groups, Factorial Experiments, Confidence Intervals.

Author(s): Javier R. Movellan

127 Pages

Notes on Probability Theory and Statistics

This note explains the following topics: Probability Theory, Random Variables, Distribution Functions, And Densities, Expectations And Moments Of Random Variables, Parametric Univariate Distributions, Sampling Theory, Point And Interval Estimation, Hypothesis Testing, Statistical Inference, Asymptotic Theory, Likelihood Function, Neyman or Ratio of the Likelihoods Tests.

Author(s): Antonis Demos

138 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

Probability and Stochastic Processes

This book covers the following topics: Basic Concepts of Probability Theory, Random Variables, Multiple Random Variables, Vector Random Variables, Sums of Random Variables and Long-Term Averages, Random Processes, Analysis and Processing of Random Signals, Markov Chains, Introduction to Queueing Theory and Elements of a Queueing System.

Author(s): Dongyu Qiu

NA Pages