First Course in Probability

ISBN-10: 0131856626
ISBN-13: 9780131856622
Edition: 7th 2006 (Revised)
Authors: Sheldon M. Ross
List price: $132.00
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Description: This introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus. Includes a software diskette, referenced in the book and packaged with each  More...

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Book details

List price: $132.00
Edition: 7th
Copyright year: 2006
Publisher: Prentice Hall PTR
Binding: Hardcover
Pages: 576
Size: 7.00" wide x 9.25" long x 1.00" tall
Weight: 2.112
Language: English

This introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus. Includes a software diskette, referenced in the book and packaged with each copy, that provides an easy-to-use tool for readers to derive probabilities for binomial. Presents new examples and exercises throughout. Offers a new section that presents an elegant way of computing the moments of random variables defined as the number of events that occur. Gives applications to binomial, hypergeometric, and negative hypergeometric random variables, as well as random variables resulting from coupon collecting and match models. Provides additional results on inclusion-exclusion identity, Poisson paradigm, multinomial distribution, and bivariate normal distribution A useful reference for engineering and science professionals.

Preface
Combinatorial Analysis
Introduction
The Basic Principle of Counting
Permutations
Combinations
Multinomial Coefficients
The Number of Integer Solutions of Equations*
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Axioms of Probability
Introduction
Sample Space and Events
Axioms of Probability
Some Simple Propositions
Sample Spaces Having Equally Likely Outcomes
Probability as a Continuous Set Function*
Probability as a Measure of Belief
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Conditional Probability and Independence
Introduction
Conditional Probabilities
Bayes' Formula
Independent Events
P(.[vertical bar]F) Is a Probability
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Random Variables
Random Variables
Discrete Random Variables
Expected Value
Expectation of a Function of a Random Variable
Variance
The Bernoulli and Binomial Random Variables
Properties of Binomial Random Variables
Computing the Binomial Distribution Function
The Poisson Random Variable
Computing the Poisson Distribution Function
Other Discrete Probability Distributions
The Geometric Random Variable
The Negative Binomial Random Variable
The Hypergeometric Random Variable
The Zeta (or Zipf) Distribution
Properties of the Cumulative Distribution Function
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Continuous Random Variables
Introduction
Expectation and Variance of Continuous Random Variables
The Uniform Random Variable
Normal Random Variables
The Normal Approximation to the Binomial Distribution
Exponential Random Variables
Hazard Rate Functions
Other Continuous Distributions
The Gamma Distribution
The Weibull Distribution
The Cauchy Distribution
The Beta Distribution
The Distribution of a Function of a Random Variable
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Jointly Distributed Random Variables
Joint Distribution Functions
Independent Random Variables
Sums of Independent Random Variables
Conditional Distributions: Discrete Case
Conditional Distributions: Continuous Case
Order Statistics
Joint Probability Distribution of Functions of Random Variables
Exchangeable Random Variables
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Properties of Expectation
Introduction
Expectation of Sums of Random Variables
Obtaining Bounds from Expectations via the Probabilistic Method
The Maximum-Minimums Identity
Moments of the Number of Events that Occur
Covariance, Variance of Sums, and Correlations
Conditional Expectation
Definitions
Computing Expectations by Conditioning
Computing Probabilities by Conditioning
Conditional Variance
Conditional Expectation and Prediction
Moment Generating Functions
Joint Moment Generating Functions
Additional Properties of Normal Random Variables
The Multivariate Normal Distribution
The Joint Distribution of the Sample Mean and Sample Variance
General Definition of Expectation
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Limit Theorems
Introduction
Chebyshev's Inequality and the Weak Law of Large Numbers
The Central Limit Theorem
The Strong Law of Large Numbers
Other Inequalities
Bounding The Error Probability
Summary
Problems
Theoretical Exercises
Self-Test Problems and Exercises
Additional Topics in Probability
The Poisson Process
Markov Chains
Surprise, Uncertainty, and Entropy
Coding Theory and Entropy
Summary
Theoretical Exercises
Self-Test Problems and Exercises
Simulation
Introduction
General Techniques for Simulating Continuous Random Variables
The Inverse Transformation Method
The Rejection Method
Simulating from Discrete Distributions
Variance Reduction Techniques
Use of Antithetic Variables
Variance Reduction by Conditioning
Control Variates
Summary
Problems
Self-Test Problems and Exercises
Appendices
Answers to Selected Problems
Solutions to Self-Test Problems and Exercises
Index

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