The contents include:
Introduction, Preliminary Results, Distributions, Random Variables,
Expectation, Independence, Weak Law of Large Numbers, Borel-Cantelli Lemmas,
Strong Law of Large Numbers, Random Series, Weak Convergence, Characteristic
Functions, Central Limit Theorems, Poisson Convergence, Stein's Method,
Random Walk Preliminaries, Stopping Times, Recurrence, Path Properties, Law
of The Iterated Logarithm.
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 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 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.