Probability Theory and Examples

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

Theory of Probability by Prof. Scott Sheffield

This note covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.

Author(s): Prof. Scott Sheffield

NA Pages

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

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