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.
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 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.
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.
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
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.