Always Learning

First Course in Probability, A, 6/E
Sheldon Ross

ISBN-10: 0130338516
ISBN-13:  9780130338518

Publisher:  Pearson
Copyright:  2002
Format:  Cloth; 528 pp
Published:  07/31/2001


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Description

For upper level or undergraduate/graduate level introduction to probability for math, science, engineering, and business students with a background in elementary calculus.

This market-leading introduction to probability features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. The outstanding problem sets and intuitive explanations are hallmark features of this market leading text.


Features

  • NEW - Subsections on the probabilistic method and the maximum-minimums identity.

    • Provides a careful explanation of complicated topics.

  • NEW - New examples—Relating to DNA matching, utility, finance, and applications of the probabilistic method.

    • Shows application of material to “real world” situations.

  • Intuitive treatment of probability—Intuitive explanations follow many examples.

    • Provides clear, complete explanations to fully explain mathematical concepts.

  • Extensive exercise sets with a wide variety and level of problems.

    • Provides students with ample opportunity to expand and test their knowledge.

  • Probability Models Disk—Included with each copy of the book.

    • Contains six probability models that are referenced in the text and allow students to quickly and easily perform calculations and simulations.


New To This Edition

  • Subsections on the probabilistic method and the maximum-minimums identity.

    • Provides a careful explanation of complicated topics.

  • New examples—Relating to DNA matching, utility, finance, and applications of the probabilistic method.

    • Shows application of material to “real world” situations.


Table of Contents

(NOTE: Each chapter concludes with Summary, Problems, Theoretical Exercises, and Self-Test Problems and Exercises.)

 1. Combinatorial Analysis.

Introduction. The Basic Principle of Counting. Permutations. Combinations. Multinomial Coefficients. The Number of Integer Solutions of Equations.



 2. 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.



 3. Conditional Probability and Independence.

Introduction. Conditional Probabilities. Bayes' Formula. Independent Events. P(•|F) is a Probability.



 4. Random Variables.

Random Variables. Discrete Random Variables. Expected Value. Expectation of a Function of a Random Variable. Variance. The Bernoulli and Binomial Random Variables. The Poisson Random Variable. Other Discrete Probability Distribution. Properties of the Cumulative Distribution Function.



 5. Continuous Random Variables.

Introduction. Expectation and Variance of Continuous Random Variables. The Uniform Random Variable. Normal Random Variables. Exponential Random Variables. Other Continuous Distributions. The Distribution of a Function of a Random Variable.



 6. 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.



 7. Properties of Expectation.

Introduction. Expectation of Sums of Random Variables. Covariance, Variance of Sums, and Correlations. Conditional Expectation. Conditional Expectation and Prediction. Moment Generating Functions. Additional Properties of Normal Random Variables. General Definition of Expectation.



 8. 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 When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson.



 9. Additional Topics in Probability.

The Poisson Process. Markov Chains. Surprise, Uncertainty, and Entropy. Coding Theory and Entropy.



10. Simulation.

Introduction. General Techniques for Simulating Continuous Random Variables. Simulating from Discrete Distributions. Variance Reduction Techniques.



Appendix A. Answers to Selected Problems.


Appendix B. Solutions to Self-Test Problems and Exercises.


Index.


Next Edition(s)

  • First Course in Probability, A, 8/E
    Ross
    ©2010  |  Pearson  |  Cloth; 552 pp  |  Instock
    ISBN-10: 013603313X  |  ISBN-13: 9780136033134
    Brief Description  |  More Info



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Companion Website-Ross, 6/E
Ross
©2002  |  Pearson  |  On-line Supplement; 0 pp  |  Live
ISBN-10: 0130340103  |  ISBN-13: 9780130340108
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In this section:

Companion Website-Ross, 6/E
Ross
©2002  |  Pearson  |  On-line Supplement; 0 pp  |  Live
ISBN-10: 0130340103  |  ISBN-13: 9780130340108
More Info

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Websites and online courses

Companion Website-Ross, 6/E
Ross
©2002  |  Pearson  |  On-line Supplement; 0 pp  |  Live
ISBN-10: 0130340103  |  ISBN-13: 9780130340108
More Info


Websites and Online Courses

Companion Website-Ross, 6/E
Ross
©2002  |  Pearson  |  On-line Supplement; 0 pp  |  Live
ISBN-10: 0130340103  |  ISBN-13: 9780130340108
More Info

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