# Fundamentals of Probability / Edition 2

ISBN-10: 0130113298

ISBN-13: 9780130113290

Pub. Date: 09/02/1999

Publisher: Prentice Hall

This book is a valuable reference to Basic Probability and related problems, featuring unique discussions published in recent journals to support individual investigation. Chapter topics include combinatorial methods, conditional probability and independence, random variables, distributions, and simulation. For professionals in the fields of computer and actuarial…  See more details below

## Overview

This book is a valuable reference to Basic Probability and related problems, featuring unique discussions published in recent journals to support individual investigation. Chapter topics include combinatorial methods, conditional probability and independence, random variables, distributions, and simulation. For professionals in the fields of computer and actuarial science, electrical and industrial engineering,, operations research, applied mathematics, and statistics, who desire additional input to help solve the indeterministic business, government, and engineering problems they encounter at work.

## Product Details

ISBN-13:
9780130113290
Publisher:
Prentice Hall
Publication date:
09/02/1999
Edition description:
Older Edition
Pages:
511
Product dimensions:
6.14(w) x 9.30(h) x 1.11(d)

## Related Subjects

 Preface xi 1 Axioms of Probability 1 1.1 Introduction 1 1.2 Sample Space and Events 4 1.3 Axioms of Probability 11 1.4 Basic Theorems 18 1.5 Continuity of Probability Function 27 1.6 Probabilities 0 and 1 29 1.7 Random Selection of Points from Intervals 31 Review Problems 35 2 Combinatorial Methods 38 2.1 Introduction 38 2.2 Counting Principle 38 Number of Subsets of a Set 42 Tree Diagrams 43 2.3 Permutations 47 2.4 Combinations 54 2.5 Stirling's Formula 70 Review Problems 72 3 Conditional Probability and Independence 75 3.1 Conditional Probability 75 Reduction of Sample Space 79 3.2 Law of Multiplication 85 3.3 Law of Total Probability 89 3.4 Bayes' Formula 99 3.5 Independence 106 Review Problems 126 4 Distribution Functions and Discrete Random Variables 129 4.1 Random Variables 129 4.2 Distribution Functions 134 4.3 Discrete Random Variables 143 4.4 Expectations of Discrete Random Variables 150 4.5 Variances and Moments of Discrete Random Variables 161 Moments 167 4.6 Standardized Random Variables 170 Review Problems 171 5 Special Discrete Distributions 174 5.1 Bernoulli and Binomial Random Variables 174 Expectations and Variances of Binomial Random Variables 180 5.2 Poisson Random Variable 188 Poisson as an Approximation to Binomial 188 Poisson Process 194 5.3 Other Discrete Random Variables 203 Geometric Random Variable 203 Negative Binomial Random Variable 205 Hypergeometric Random Variable 207 Review Problems 215 6 Continuous Random Variables 218 6.1 Probability Density Functions 218 6.2 Density Function of a Function of a Random Variable 227 6.3 Expectations and Variances 233 Expectations of Continuous Random Variables 233 Variances of Continuous Random Variables 239 Review Problems 245 7 Special Continuous Distributions 247 7.1 Uniform Random Variable 247 7.2 Normal Random Variable 254 Correction for Continuity 257 7.3 Exponential Random Variable 269 7.4 Gamma Distribution 276 7.5 Beta Distribution 281 Review Problems 285 8 Joint distributions 287 8.1 Bivariate Distributions 287 Joint Probability Functions 287 Joint Probability Density Functions 290 8.2 Independent Random Variables 305 8.3 Conditional Distributions 316 8.4 Multivariate Distributions 329 8.5 Order Statistics 345 8.6 Multinomial Distributions 352 8.7 Transformations of Two Random Variables 356 Review Problems 362 9 More Expectations and Variances 367 9.1 Expected Values of Sums of Random Variables 367 Pattern Appearance 376 9.2 Covariance 383 9.3 Correlation 392 9.4 Conditioning on Random Variables 397 9.5 Bivariate Normal Distribution 408 Review Problems 414 10 Sums of Independent Random Variables and Limit Theorems 416 10.1 Moment-Generating Functions 416 10.2 Sums of Independent Random Variables 427 10.3 Markov and Chebyshev Inequalities 437 10.4 Laws of Large Numbers 443 10.5 Central Limit Theorem 452 Review Problems 458 11 Simulation 461 11.1 Introduction 461 11.2 Simulation of Combinatorial Problems 466 11.3 Simulation of Conditional Probabilities 469 11.4 Simulation of Random Variables 473 11.5 Monte Carlo Method 481 Appendix Tables 487 Answers to Odd-Numbered Exercises 491 Index 501