Fundamentals Probability / Edition 1

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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.
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Editorial Reviews

Booknews
This one-semester basic probability textbook is written for majors in mathematics, physics, engineering, statistics, actuarial science, operations research, and computer science. The revised edition adds a subsection on reliability of systems and a section on order statistics to the chapter on joint distributions. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780130657985
  • Publisher: Prentice Hall Professional Technical Reference
  • Publication date: 9/28/1995
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 512
  • Product dimensions: 6.32 (w) x 9.31 (h) x 1.11 (d)

Table of Contents

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
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