Course in Probability / Edition 1

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Overview

This text is intended primarily for readers interested in mathematical probability as applied to mathematics, statistics, operations research, engineering, and computer science. It is also appropriate for mathematically oriented readers in the physical and social sciences. Prerequisite material consists of basic set theory and a firm foundation in elementary calculus, including infinite series, partial differentiation, and multiple integration. Some exposure to rudimentary linear algebra (e.g., matrices and determinants) is also desirable. This text includes pedagogical techniques not often found in books at this level, in order to make the learning process smooth, efficient, and enjoyable.

Fundamentals of Probability: Probability Basics. Mathematical Probability. Combinatorial Probability. Conditional Probability and Independence. Discrete Random Variables: Discrete Random Variables and Their Distributions. Jointly Discrete Random Variables. Expected Value of Discrete Random Variables. Continuous Random Variables: Continuous Random Variables and Their Distributions. Jointly Continuous Random Variables. Expected Value of Continuous Random Variables. Limit Theorems and Advanced Topics: Generating Functions and Limit Theorems. Additional Topics.

For all readers interested in probability.

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Product Details

  • ISBN-13: 9780201774719
  • Publisher: Pearson
  • Publication date: 12/10/2004
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 816
  • Sales rank: 253,424
  • Product dimensions: 7.40 (w) x 9.00 (h) x 1.90 (d)

Table of Contents

(Chapter Opener and Review appear in each chapter).

I. FUNDAMENTALS OF PROBABILITY.

1. Probability Basics.

Biography: Girolamo Cardano.

From Percentages to Probabilities.

Set Theory.

2. Mathematical Probability.

Biography: Andrei Kolmogorov.

Sample Space and Events.

Axioms of Probability.

Specifying Probabilities.

Basic Properties of Probability.

3. Combinatorial Probability.

Biography: James Bernoulli.

The Basic Counting Rule.

Permutations and Combinations.

Applications of Counting Rules to Probability.

4. Conditional Probability and Independence.

Biography: Thomas Bayes.

Conditional Probability.

The General Multiplication Rule.

Independent Events.

Bayes' Rule.

II. DISCRETE RANDOM VARIABLES.

5. Discrete Random Variables and Their Distributions.

Biography: Siméon-Dennis Poisson.

From Variables to Random Variables.

Probability Mass Functions.

Binomial Random Variables.

Hypergeometric Random Variables.

Poisson Random Variables.

Geometric Random Variables.

Other Important Discrete Random Variables.

Functions of a Discrete Random Variable.

6. Jointly Discrete Random Variables.

Biography: Blaise Pascal.

Joint and Marginal Probability Mass Functions: Bivariate Case.

Joint and Marginal Probability Mass Functions: Multivariate Case.

Conditional Probability Mass Functions.

Independent Random Variables.

Functions of Two or More Discrete Random Variables.

Sums of Discrete Random Variables.

7. Expected Value of Discrete Random Variables.

Biography: Christiaan Huygens.

From Averages to Expected Values.

Basic Properties of Expected Value.

Variance of Discrete Random Variables.

Variance, Covariance, and Correlation.

Conditional Expectation.

III. CONTINUOUS RANDOM VARIABLES.

8. Continuous Random Variables and Their Distributions.

Biography: Carl Friedrich Gauss.

Introducing Continuous Random Variables.

Cumulative Distribution Functions.

Probability Density Functions.

Uniform and Exponential Random Variables.

Normal Random Variables.

Other Important Continuous Random Variables.

Functions of a Continuous Random Variable.

9. Jointly Continuous Random Variables.

Biography: Pierre de Fermat.

Joint Cumulative Distribution Functions.

Introducing Joint Probability Density Functions.

Basic Properties of Joint Probability Density Functions.

Marginal and Conditional Probability Density Functions.

Independent Continuous Random Variables.

Functions of Two or More Continuous Random Variables.

Sums and Quotients of Continuous Random Variables.

Multidimensional Transformation Theorem.

10. Expected Value of Continuous Random Variables.

Biography: Pafnuty Chebyshev.

Expected Value of a Continuous Random Variable.

Basic Properties of Expected Value.

Variance, Covariance, and Correlation.

Conditional Expectation.

The Bivariate Normal Distribution.

IV. LIMIT THEOREMS AND ADVANCED TOPICS.

11. Generating Functions and Limit Theorems.

Biography: William Feller.

Moment Generating Functions.

Joint Moment Generating Functions.

Laws of Large Numbers.

The Central Limit Theorem.

12. Additional Topics.

Biography: Sir Ronald Fisher.

The Poisson Process.

Basic Queueing Theory.

The Multivariate Normal Distribution.

Sampling Distributions.

Appendices.

Index.

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  • Posted April 14, 2010

    A Gem from Prof.Weiss

    Would you like to know the answers for WHAT,WHY,HOW and FROM WHERE in Probability concepts ? Then choose this wonderful book of Prof.Weiss. I have come across so many books and each of these does its job in its own way. However I have found a single book that asnwers all the above questions.
    Prof.Weiss claims in his preface that this book is not ordinary probability book. When I read this line in the book shop, I felt funny and thought this is going to be one among several books sleeping in my shelf.I bought it just because it was so cheap. What a wonder ! The contents exactly matched his claim. This is not really an ordinary probability book. But a Gem!

    Beginners who would like to know the inner details of probability from basics, must go for this book. Those guys who are planning to go back to school after long gap like me(I am back to school after 8 years of professional job) can easily go for this one.
    I have so many books on probability and wasted lot of time and efforts in reading those to understand the concepts clearly. This book will help you to make a great leap forward to bypass so many books in the market to take up most advanced probability.

    Prof.Weiss, I thank you very much for your Gem!!!

    Was this review helpful? Yes  No   Report this review
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