Probability: Elements of the Mathematical Theory

by C. R. Heathcote

Overview

Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.

Product Details

ISBN-13:	9780486153407
Publisher:	Dover Publications
Publication date:	03/30/2012
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	288
File size:	15 MB
Note:	This product may take a few minutes to download.

Table of Contents

Preface
Principal notations
1 PROBABILITY SPACES AND RANDOM VARIABLES
1.1 Probability spaces
1.2 Properties of probability spaces
1.3 Finite probability spaces
1.4 Random variables
1.5 Expectation and moments
Appendix Monotone sequences of events
2 SOME REAL VARIABLE THEORY
2.1 Taylor's Theorem
2.2 Power series and probability generating functions
2.3 Integral transforms
2.4 Transformations
2.5 Special functions
Table of generating functions
3 SEVERAL RANDOM VARIABLES
3.1 Joint distributions
3.2 Conditional probability
3.3 Independent random variables
3.4* Bayes's Theorem
3.5* Sequences of dependent random variables; Markov chains
4 WEAK CONVERGENCE
4.1 Sequences of distribution functions
4.2 The weak law of large numbers
4.3 The central limit theorem
4.4* Distributions derived from the normal
4.5* Some limit theorems for Markov chains
5 ALMOST SURE CONVERGENCE
5.1 Infinite sequences of events
5.2 Almost sure convergence
5.3 The strong law of large numbers
5.4* The strong law (continued)
5.5* Occupation times and recurrent Markov chains
Answers to selected exercises
Index