Basic Probability Theory

Name: Basic Probability Theory
Price: 6.75 USD
Availability: InStock
ISBN: 9780486466286

ISBN-10: 0486466280

ISBN-13: 9780486466286

Edition: 2008

Authors: Robert B. Ash

List price: $22.95

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Description:

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.

Book details

List price: $22.95
Copyright year: 2008
Publisher: Dover Publications, Incorporated
Publication date: 6/26/2008
Binding: Paperback
Pages: 352
Size: 5.47" wide x 8.46" long x 0.71" tall
Weight: 1.012
Language: English




Basic Concepts



Introduction



Algebra of Events (Boolean Algebra)



Probability



Combinatorial Problems



Independence



Conditional Probability



Some Fallacies in Combinatorial Problems



Appendix: Stirling's Formula



Random Variables



Introduction



Definition of a Random Variable



Classification of Random Variables



Functions of a Random Variable



Properties of Distribution Functions



Joint Density Functions



Relationship Between Joint and Individual Densities; Independence of Random Variables



Functions of More Than One Random Variable



Some Discrete Examples



Expectation



Introduction



Terminology and Examples



Properties of Expectation



Correlation



The Method of Indicators



Some Properties of the Normal Distribution



Chebyshev's Inequality and the Weak Law of Large Numbers



Conditional Probability and Expectation



Introduction



Examples



Conditional Density Functions



Conditional Expectation



Appendix: The General Concept of Conditional Expectation



Characteristic Functions



Introduction



Examples



Properties of Characteristic Functions



The Central Limit Theorem



Infinite Sequences of Random Variables



Introduction



The Gambler's Ruin Problem



Combinatorial Approach to the Random Walk; the Reflection Principle



Generating Functions



The Poisson Random Process



The Strong Law of Large Numbers



Markov Chains



Introduction



Stopping Times and the Strong Markov Property



Classification of States



Limiting Probabilities



Stationary and Steady-State Distributions



Introduction to Statistics



Statistical Decisions



Hypothesis Testing



Estimation



Sufficient Statistics



Unbiased Estimates Based on a Complete Sufficient Statistic



Sampling from a Normal Population



The Multidimensional Gaussian Distribution


Tables


A Brief Bibliography


Solutions to Problems


Index