Fundamentals of Probability,9780130113290

Fundamentals of Probability

by
Edition: 3rd
ISBN13: 9780130113290
ISBN10: 0130113298
Format: Hardcover
Pub. Date: 2005-01-01
Publisher(s): Prentice Hall
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Summary

Comprehensive and class-tested, this book is designed for a course in Basic Probability to be taken by mathematics, physics, engineering, statistics, actuarial science, operations research, and computer science majors. It assumes a second course in calculus. The aim of the book is to present probability in the most natural way: through a great number of attractive and instructive examples and exercises that motivate the definitions, theorems, and methodology of the theory. Examples and exercises have been very carefully designed to arouse students' curiosity, motivating them to delve into the theory with enthusiasm. Unique discussions of probability problems published in recent journals are featured to stimulate classroom discussion or individual investigation.

Table of Contents

Preface xi
Axioms of Probability
1(37)
Introduction
1(3)
Sample Space and Events
4(7)
Axioms of Probability
11(7)
Basic Theorems
18(9)
Continuity of Probability Function
27(2)
Probabilities 0 and 1
29(2)
Random Selection of Points from Intervals
31(7)
Review Problems
35(3)
Combinatorial Methods
38(37)
Introduction
38(1)
Counting Principle
38(9)
Number of Subsets of a Set
42(1)
Tree Diagrams
43(4)
Permutations
47(7)
Combinations
54(16)
Stirling's Formula
70(5)
Review Problems
72(3)
Conditional Probability and Independence
75(54)
Conditional Probability
75(10)
Reduction of Sample Space
79(6)
Law of Multiplication
85(4)
Law of Total Probability
89(10)
Bayes' Formula
99(7)
Independence
106(23)
Review Problems
126(3)
Distribution Functions and Discrete Random Variables
129(45)
Random Variables
129(5)
Distribution Functions
134(9)
Discrete Random Variables
143(7)
Expectations of Discrete Random Variables
150(11)
Variances and Moments of Discrete Random Variables
161(9)
Moments
167(3)
Standardized Random Variables
170(4)
Review Problems
171(3)
Special Discrete Distributions
174(44)
Bernoulli and Binomial Random Variables
174(14)
Expectations and Variances of Binomial Random Variables
180(8)
Poisson Random Variable
188(15)
Poisson as an Approximation to Binomial
188(6)
Poisson Process
194(9)
Other Discrete Random Variables
203(15)
Geometric Random Variable
203(2)
Negative Binomial Random Variable
205(2)
Hypergeometric Random Variable
207(8)
Review Problems
215(3)
Continuous Random Variables
218(29)
Probability Density Functions
218(9)
Density Function of a Function of a Random Variable
227(6)
Expectations and Variances
233(14)
Expectations of Continuous Random Variables
233(6)
Variances of Continuous Random Variables
239(6)
Review Problems
245(2)
Special Continuous Distributions
247(40)
Uniform Random Variable
247(7)
Normal Random Variable
254(15)
Correction for Continuity
257(12)
Exponential Random Variable
269(7)
Gamma Distribution
276(5)
Beta Distribution
281(6)
Review Problems
285(2)
Joint distributions
287(80)
Bivariate Distributions
287(18)
Joint Probability Functions
287(3)
Joint Probability Density Functions
290(15)
Independent Random Variables
305(11)
Conditional Distributions
316(13)
Multivariate Distributions
329(16)
Order Statistics
345(7)
Multinomial Distributions
352(4)
Transformations of Two Random Variables
356(11)
Review Problems
362(5)
More Expectations and Variances
367(49)
Expected Values of Sums of Random Variables
367(16)
Pattern Appearance†
376(7)
Covariance
383(9)
Correlation
392(5)
Conditioning on Random Variables
397(11)
Bivariate Normal Distribution
408(8)
Review Problems
414(2)
Sums of Independent Random Variables and Limit Theorems
416(45)
Moment-Generating Functions
416(11)
Sums of Independent Random Variables
427(10)
Markov and Chebyshev Inequalities
437(6)
Laws of Large Numbers
443(9)
Central Limit Theorem
452(9)
Review Problems
458(3)
Simulation
461(26)
Introduction
461(5)
Simulation of Combinatorial Problems
466(3)
Simulation of Conditional Probabilities
469(4)
Simulation of Random Variables
473(8)
Monte Carlo Method
481(6)
Appendix Tables 487(4)
Answers to Odd-Numbered Exercises 491(10)
Index 501

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