The contents include:
Introduction, Preliminary Results, Distributions, Random Variables,
Expectation, Independence, Weak Law of Large Numbers, Borel-Cantelli Lemmas,
Strong Law of Large Numbers, Random Series, Weak Convergence, Characteristic
Functions, Central Limit Theorems, Poisson Convergence, Stein's Method,
Random Walk Preliminaries, Stopping Times, Recurrence, Path Properties, Law
of The Iterated Logarithm.
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.
These notes are intended to
give a solid introduction to Probability Theory with a reasonable level of
mathematical rigor. Topics covered includes: Elementary probability,
Discrete-time finite state Markov chains, Existence of Markov Chains,
Discrete-time Markov chains with countable state space, Probability triples,
Limit Theorems for stochastic sequences, Moment Generating Function, The Central
Limit Theorem, Measure Theory and Applications.
This book presents the basic
ideas of the subject and its application to a wider audience. Topics covered
includes: The Ising model, Markov fields on graphs, Finite lattices, Dynamic
models, The tree model and Additional applications.
This text assumes no prerequisites in probability, a basic exposure to
calculus and linear algebra is necessary. Some real analysis as well as some
background in topology and functional analysis can be helpful. This note covers
the following topics: Limit theorems, Probability spaces, random variables,
independence, Markov operators, Discrete Stochastic Processes, Continuous
Stochastic Processes, Random Jacobi matrices, Symmetric Diophantine Equations
and Vlasov dynamics.
This note provides an introduction to probability theory and
mathematical statistics that emphasizes the probabilistic foundations required
to understand probability models and statistical methods. Topics covered
includes the probability axioms, basic combinatorics, discrete and continuous
random variables, probability distributions, mathematical expectation, common
families of probability distributions and the central limit theorem.