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 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 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