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.
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 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.
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 book is addressed to readers who
are already familiar with applied mathematics at the advanced undergraduate level or preferably higher. Topics covered
includes: Plausible Reasoning, Quantitative Rules, Elementary Sampling Theory,
Elementary Hypothesis Testing, Queer Uses For Probability Theory, Elementary
Parameter Estimation, Central, Gaussian Or Normal Distribution.