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 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 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.