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INTRODUCTION TOPROBABILITYAND
SCIENTISTS AND ENGINEERS
Walter A. Rosenkrantz
Department of Mathematics and StatisticsUniversity of Massachusetts at Amherst
The McGraw-Hill Companies, Inc.New York St. Louis San Francisco Auckland Bogota CaracasLisbon London Madrid Mexico City Milan Montreal New DelhiSan Juan Singapore Sydney Tokyo Toronto
CONTENTS
PREFACE
CHAPTER 1
CHAPTER 2
DATA ANALYSIS
1.1 Orientation
1.2 The Role and Scope of Statistics in Scienceand Engineering
1.3 Data Defined on a Population
1.4 The Frequency Distribution of a Variable Definedon a PopulationProblems
1.5 Quantiles of a Distribution
Problems
1.6 Measures of Location (Central Value)and Variability
Problems
1.7 Mathematical Details and Derivations
1.8 Chapter Summary
PROBABILITY THEORY
2.1 Orientation
2.2 Sample Space, Events, and Axiomsof Probability TheoryProblems
2.3 Mathematical Models of Random Sampling
Problems ^:.
2.4 Conditional Probability, Bayes' Theorem,and Independence •'-Problems
2.5 The Binomial Theorem (Optional)
2.6 Chapter Summary :
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88V
VI Contents
C H A P T E R 3
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DISCRETE RANDOM VARIABLESAND THEIR DISTRIBUTION FUNCTIONS
3.1 Orientation
3.2 Discrete Random Variables
Problems
3.3 Expected Value and Variance of a Random Variable
Problems
3.4 The Hypergeometric Distribution3.5 The Binomial Distribution
Problems
3.6 The Poisson Distribution
Problems
3.7 Mathematical Details and Derivations
3.8 Chapter Summary
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135
CHAPTER 4 CONTINUOUS RANDOM VARIABLESAND THEIR DISTRIBUTION FUNCTIONS 136
4.14.2
4.3
4.4
4.5
4.6
4.7
4.8
OrientationDefinition and Examples of Continuous RandomVariables
Problems
Expected Value, Moments, and Varianceof a Continuous Random Variable
ProblemsThe Normal Distribution
Problems
Other Important Continuous Distributions
ProblemsFunctions of a Random Variable
Problems
Mathematical Details and Derivations
Chapter Summary
136
137
143
146148
149
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172
CHAPTER 5 MULTIVARIATE PROBABILITY DISTRIBUTIONS
Contents vii
173
5.15.2
5.3
5.4
5.5
5.6
5.7
5.8
OrientationThe Joint Probability Function
Problems
Problems
The Multinomial Distribution
The Poisson Process
Applications of Bernoulli Random Variablesto Reliability Theory (Optional)
Problems
The Joint Density Function (Continuous Case)
Problems
Mathematical Details and Derivations
Chapter Summary
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181
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217
CHAPTER 6 SAMPLING DISTRIBUTION THEORY 218
6.1 Orientation
6.2 Sampling From a Normal Distribution
Problems
6.3 The Gamma Distribution
6.4 The Distribution of the Sample Variance
Problems
6.5 Mathematical Details and Derivations
6.6 Chapter Summary
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CHAPTER 7 POINT AND INTERVAL ESTIMATION 243
7.17.2
7.3
OrientationPoint Estimation of the Mean and Variance
Confidence Intervals for the Meanand Variance
Problems
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256
viii Contents
7.4 Point and Interval Estimation for the Differenceof Two Means
Problems
7.5 Point and Interval Estimationfor a Population Proportion
Problems
7.6 Some Methods of Estimation(Optional)
Problems7.7 Chapter Summary
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CHAPTER 8 INFERENCES ABOUT POPULATION MEANS 279
8.1 Orientation
8.2 Tests of Statistical Hypotheses: Basic Conceptsand Examples
Problems
8.3 Tests of Hypotheses on /u,i — yuz
Problems
8.4 Normal Probability Plots
Problems
8.5 Chapter Summary
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280
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321
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CHAPTER 9 INFERENCES ABOUT POPULATION PROPORTIONS 327
9.1 Orientation9.2 Tests Concerning the Parameter p
of a Binomial Distribution
Problems
9.3 Chi-Square Test
9.4 Contingency Tables
Problems
9.5 Chapter Summary
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351
Contents ix
CHAPTER 10 LINEAR REGRESSION AND CORRELATION 352
10.1 Orientation 352
10.2 Method of Least Squares 353
Problems 363
10.3 The Simple Linear Regression Model 366
Problems 382
10.4 Model Checking 386
Problems 396
10.5 Mathematical Details and Derivations 399
Problems 404
10.6 Chapter Summary 404
CHAPTER 11 MULTIPLE LINEAR REGRESSION 406
11.1 Orientation 406
11.2 The Matrix Approach to Simple Linear Regression 407
Problems 417
11.3 The Matrix Approach to Multiple Linear Regression 418
Problems 432
11.4 Mathematical Details and Derivations 435
11.5 Chapter Summary 435
CHAPTER 12 SINGLE-FACTOR EXPERIMENTS:ANALYSIS OF VARIANCE 437
12.1 Orientation 437
12.2 The Single-Factor ANOVA Model 438
Problems 453
12.3 Confidence Intervals for the Treatment Means; Contrasts 456
Problems 462
12.4 Random Effects Model 464
Problems 466
12.5 Chapter Summary 468
X Contents
CHAPTER 1 3 DESIGN AND ANALYSISOF MULTIFACTOR EXPERIMENTS 469
13.1 Orientation
13.2 Randomized Complete Block Designs
Problems13.3 Two-Factor Experiments with n > 1 Observations
Per Cell
Problems
13.4 2k Factorial Designs (Optional)
Problems
13.5 Chapter Summary
CHAPTER 14 STATISTICAL QUALITY CONTROL
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525
14.1 Orientation
14.2 x and R Control Charts
14.3 p Charts and c Charts
Problems
14.4 Chapter Summary
Appendix A TablesAnswers to Odd-Numbered ProblemsIndex
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539
541
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565
583
