The Role of Statistics in Engineering 1 in .NET

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The Engineering Method and Statistical Thinking 2 Collecting Engineering Data 5
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1-2.1 Basic Principles 5 1-2.2 Retrospective Study 5 1-2.3 Observational Study 6 1-2.4 Designed Experiments 6 1-2.5 A Factorial Experiment for the Connector Pull-Off Force Problem (CD Only) 8 1-2.6 Observing Processes Over Time 8
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Cumulative Distribution Functions 63 Mean and Variance of a Discrete Random Variable 66 Discrete Uniform Distribution 70 Binomial Distribution 72 Geometric and Negative Binomial Distributions 78
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3-7.1 Geometric Distribution 78 3-7.2 Negative Binomial Distribution 80
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Hypergeometric Distribution 84 Poisson Distribution 89
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Mechanistic and Empirical Models 11 Probability and Probability Models 14
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Probability 16
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Continuous Random Variables and Probability Distributions 97
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2-1.1 Random Experiments 17 2-1.2 Sample Spaces 18 2-1.3 Events 22 2-1.4 Counting Techniques (CD Only) 25
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Interpretations of Probability 27
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2-2.1 Introduction 27 2-2.2 Axioms of Probability 30
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Addition Rules 33 Conditional Probability 37 Multiplication and Total Probability Rules 42
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Independence 46 Bayes Theorem 51 Random Variables 53
Discrete Random Variables and Probability Distributions 59
Continuous Random Variables 98 4-2 Probability Distributions and Probability Density Functions 98 4-3 Cumulative Distribution Functions 102 4-4 Mean and Variance of a Continuous Random Variable 105 4-5 Continuous Uniform Distribution 107 4-6 Normal Distribution 109 4-7 Normal Approximation to the Binomial and Poisson Distributions 118 4-8 Continuity Corrections to Improve the Approximation (CD Only) 122 4-9 Exponential Distribution 122 4-10 Erlang and Gamma Distribution 128
4-10.1 Erlang Distribution 128 4-10.2 Gamma Distribution 130
3-1 3-2
Discrete Random Variables 60 Probability Distributions and Probability Mass Functions 61
4-11 Weibull Distribution 133 4-12 Lognormal Distribution 135
CONTENTS
Joint Probability Distributions 141
5-1.1 Joint Probability Distributions 142 5-1.2 Marginal Probability Distributions 144 5-1.3 Conditional Probability Distributions 146 5-1.4 Independence 148
CHAPTER 7 Point Estimation of
Parameters 220
7-1 7-2 Introduction 221 General Concepts of Point Estimation 222
7-2.1 Unbiased Estimators 222 7-2.2 Proof that S is a Biased Estimator of (CD Only) 224 7-2.3 Variance of a Point Estimator 224 7-2.4 Standard Error: Reporting a Point Estimator 225 7-2.5 Bootstrap Estimate of the Standard Error (CD Only) 226 7-2.6 Mean Square Error of an Estimator 226
Two Discrete Random Variables 142
Multiple Discrete Random Variables 151
5-2.1 Joint Probability Distributions 151 5-2.2 Multinomial Probability Distribution 154
Methods of Point Estimation 229
7-3.1 Method of Moments 229 7-3.2 Method of Maximum Likelihood 230 7-3.3 Bayesian Estimation of Parameters (CD Only) 237
Two Continuous Random Variables 157
5-3.1 Joint Probability Distributions 157 5-3.2 Marginal Probability Distributions 159 5-3.3 Conditional Probability Distributions 162 5-3.4 Independence 164
7-4 7-5
Sampling Distributions 238 Sampling Distribution of Means 239
Multiple Continuous Random Variables 167 5-5 Covariance and Correlation 171 5-6 Bivariate Normal Distribution 177 5-7 Linear Combinations of Random Variables 180 5-8 Functions of Random Variables (CD Only) 185 5-9 Moment Generating Functions (CD Only) 185 5-10 Chebyshev s Inequality (CD Only) 185
CHAPTER 8 Statistical Intervals
for a Single Sample 247
8-1 8-2 Introduction 248 Con dence Interval on the Mean of a Normal Distribution, Variance Known 249
8-2.1 Development of the Con dence Interval and Its Basic Properties 249 8-2.2 Choice of Sample Size 252 8-2.3 One-sided Con dence Bounds 253 8-2.4 General method to Derive a Con dence Interval 253 8-2.5 A Large-Sample Con dence Interval for 254 8-2.6 Bootstrap Con dence Intervals (CD Only) 256
6-1 6-2 6-3 6-4
Random Sampling and Data Description 189
Data Summary and Display 190 Random Sampling 195 Stem-and-Leaf Diagrams 197 Frequency Distributions and Histograms 203 6-5 Box Plots 207 6-6 Time Sequence Plots 209 6-7 Probability Plots 212 6-8 More About Probability Plotting (CD Only) 216
Con dence Interval on the Mean of a Normal Distribution, Variance Unknown 257
8-3.1 The t Distribution 258 8-3.2 Development of the t Distribution (CD Only) 259 8-3.3 The t Con dence Interval on 259
CONTENTS
8-5 8-6 8-7
Con dence Interval on the Variance and Standard Deviation of a Normal Distribution 261 A Large-Sample Con dence Interval for a Population Proportion 265 A Prediction Interval for a Future Observation 268 Tolerance Intervals for a Normal Distribution 270
Tests on a Population Proportion 310
9-5.1 Large-Sample Tests on a Proportion 310 9-5.2 Small-Sample Tests on a Proportion (CD Only) 312 9-5.3 Type II Error and Choice of Sample Size 312
9-6 9-7 9-8
Tests of Hypotheses for a Single Sample 277
9-1.1 Statistical Hypotheses 278 9-1.2 Tests of Statistical Hypotheses 280 9-1.3 One-Sided and Two-Sided Hypotheses 286 9-1.4 General Procedure for Hypothesis Testing 287
Summary of Inference Procedures for a Single Sample 315 Testing for Goodness of Fit 315 Contingency Table Tests 320
Hypothesis Testing 278
Statistical Inference for Two Samples 327
10-1 Introduction 328 10-2 Inference For a Difference in Means of Two Normal Distributions, Variances Known 328
10-2.1 Hypothesis Tests for a Difference in Means, Variances Known 329 10-2.2 Choice of Sample Size 331 10-2.3 Identifying Cause and Effect 333 10-2.4 Con dence Interval on a Difference in Means, Variances Known 334
Tests on the Mean of a Normal Distribution, Variance Known 289
9-2.1 Hypothesis Tests on the Mean 289 9-2.2 P-Values in Hypothesis Tests 292 9-2.3 Connection Between Hypothesis Tests and Con dence Intervals 293 9-2.4 Type II Error and Choice of Sample Size 293 9-2.5 Large Sample Test 297 9-2.6 Some Practical Comments on Hypothesis Tests 298