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

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.

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

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.

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

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.

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.

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.

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