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NI NTH E dIT Io N
Probability and Statistics
for Engineering
and the Sciences
Jay Devore
California Polytechnic State University, San Luis Obispo
Australia Brazil Mexico Singapore
United Kingdom United States
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Probability and Statistics for Engineering
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Jay L. Devore
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To my beloved grandsons
Philip and Elliot, who are
highly statistically significant.
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Contents
1 Overview and Descriptive Statistics
Introduction 1
1.1 Populations, Samples, and Processes 3
1.2 Pictorial and Tabular Methods in Descriptive Statistics 13
1.3 Measures of Location 29
1.4 Measures of Variability 36
Supplementary Exercises 47
Bibliography 51
2 Probability
Introduction 52
2.1 Sample Spaces and Events 53
2.2 Axioms, Interpretations,
and Properties of Probability 58
2.3 Counting Techniques 66
2.4 Conditional Probability 75
2.5 Independence 85
Supplementary Exercises 91
Bibliography 94
3 Discrete Random Variables and Probability
Distributions
Introduction 95
3.1 Random Variables 96
3.2 Probability Distributions for Discrete Random Variables 99
3.3 Expected Values 109
3.4 The Binomial Probability Distribution 117
3.5 Hypergeometric and Negative Binomial Distributions 126
3.6 The Poisson Probability Distribution 131
Supplementary Exercises 137
Bibliography 140
vii
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viii
Contents
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4 Continuous Random Variables and Probability
Distributions
Introduction 141
4.1 Probability Density Functions 142
4.2 Cumulative Distribution Functions
and Expected Values 147
4.3 The Normal Distribution 156
4.4 The Exponential and Gamma Distributions 170
4.5 Other Continuous Distributions 177
4.6 Probability Plots 184
Supplementary Exercises 193
Bibliography 197
5 Joint Probability Distributions
and Random Samples
Introduction 198
5.1 Jointly Distributed Random Variables 199
5.2 Expected Values, Covariance, and Correlation 213
5.3 Statistics and Their Distributions 220
5.4 The Distribution of the Sample Mean 230
5.5 The Distribution of a Linear Combination 238
Supplementary Exercises 243
Bibliography 246
6 Point Estimation
Introduction 247
6.1 Some General Concepts of Point Estimation 248
6.2 Methods of Point Estimation 264
Supplementary Exercises 274
Bibliography 275
7 Statistical Intervals Based on a Single Sample
Introduction 276
7.1 Basic Properties of Confidence Intervals 277
7.2 Large-Sample Confidence Intervals
for a Population Mean and Proportion 285
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