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.
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.
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 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.
The goal to to help the student figure out the meaning of various
concepts in Probability Theory and to illustrate them with examples. Topics
covered includes: Modelling Uncertainty, Probability Space, Conditional
Probability and Independence, Random Variable, Conditional Expectation, Gaussian
Random Variables, Limits of Random Variables, Filtering Noise and Markov Chains