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.
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 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.
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.