Page 18 - Applied statistics and probability for engineers
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Contents
Inside Front cover Index of Applications Chapter 4 Continuous Random Variables
Examples and Exercises and Probability Distributions 107
4-1 Continuous Random Variables 108
Chapter 1 The Role of Statistics in Engineering 1 4-2 Probability Distributions and Probability
Density Functions 108
1-1 The Engineering Method and Statistical 4-3 Cumulative Distribution Functions 112
Thinking 2
1-2 Collecting Engineering Data 4 4-4 Mean and Variance of a Continuous
Random Variable 114
1-2.1 Basic Principles 4 4-5 Continuous Uniform Distribution 116
1-2.2 Retrospective Study 5 4-6 Normal Distribution 119
1-2.3 Observational Study 5 4-7 Normal Approximation to the Binomial and
1-2.4 Designed Experiments 6 Poisson Distributions 128
1-2.5 Observing Processes Over Time 8
1-3 Mechanistic and Empirical Models 11 4-8 Exponential Distribution 133
Erlang and Gamma Distributions 139
4-9
1-4 Probability and Probability Models 12
4-10 Weibull Distribution 143
Chapter 2 Probability 15 4-11 Lognormal Distribution 145
4-12 Beta Distribution 148
2-1 Sample Spaces and Events 16
2-1.1 Random Experiments 16 Chapter 5 Joint Probability Distributions 155
2-1.2 Sample Spaces 17
2-1.3 Events 20 5-1 Two or More Random Variables 156
2-1.4 Counting Techniques 22 5-1.1 Joint Probability Distributions 156
2-2 Interpretations and Axioms of Probability 30 5-1.2 Marginal Probability Distributions 159
2-3 Addition Rules 35 5-1.3 Conditional Probability Distributions 161
2-4 Conditional Probability 40 5-1.4 Independence 164
2-5 Multiplication and Total Probability 5-1.5 More Than Two Random Variables 167
Rules 45 5-2 Covariance and Correlation 174
2-6 Independence 49 5-3 Common Joint Distributions 179
#BZFT 5IFPSFN 5-3.1 Multinomial Probability Distribution 179
2-8 Random Variables 57 5-3.2 Bivariate Normal Distribution 181
5-4 Linear Functions of Random Variables 184
Chapter 3 Discrete Random Variables and 5-5 General Functions of Random Variables 188
Probability Distributions 65 5-6 Moment-Generating Functions 191
3-1 Discrete Random Variables 66
Chapter 6 Descriptive Statistics 199
3-2 Probability Distributions and Probability Mass
Functions 67 6-1 Numerical Summaries of Data 200
3-3 Cumulative Distribution Functions 71 6-2 Stem-and-Leaf Diagrams 206
3-4 Mean and Variance of a Discrete Random 6-3 Frequency Distributions and Histograms 213
Variable 74 6-4 Box Plots 217
3-5 Discrete Uniform Distribution 78 6-5 Time Sequence Plots 219
3-6 Binomial Distribution 80 6-6 Scatter Diagrams 225
3-7 Geometric and Negative Binomial 6-7 Probability Plots 230
Distributions 86 Chapter 7 Point Estimation of Parameters and
3-7.1 Geometric Distribution 86 Sampling Distributions 239
3-8 Hypergeometric Distribution 93
3-9 Poisson Distribution 98 7-1 Point Estimation 240
