Applied Statistics and Probability for Engineers, EMEA Edition - Douglas C. Montgomery

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Résumé :

1 The Role of Statistics in Engineering 1

1.1 The Engineering Method and Statistical Thinking 2

1.1.1 Variability 3

1.1.2 Populations and Samples 5

1.2 Collecting Engineering Data 5

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 Observing Processes over Time 9

1.3 Mechanistic and Empirical Models 12

1.4 Probability and Probability Models 15

2 Probability 17

2.1 Sample Spaces and Events 18

2.1.1 Random Experiments 18

2.1.2 Sample Spaces 19

2.1.3 Events 21

2.2 Counting Techniques 23

2.3 Interpretations and Axioms of Probability 26

2.4 Unions of Events and Addition Rules 29

2.5 Conditional Probability 31

2.6 Intersections of Events and Multiplication and Total Probability Rules 34

2.7 Independence 36

2.8 Bayes' Theorem 39

2.9 Random Variables 40

3 Discrete Random Variables and Probability Distributions 42

3.1 Probability Distributions and Probability Mass Functions 43

3.2 Cumulative Distribution Functions 45

3.3 Mean and Variance of a Discrete Random Variable 47

3.4 Discrete Uniform Distribution 49

3.5 Binomial Distribution 51

3.6 Geometric and Negative Binomial Distributions 55

3.7 Hypergeometric Distribution 59

3.8 Poisson Distribution 63

4 Continuous Random Variables and Probability Distributions 66

4.1 Probability Distributions and Probability Density Functions 67

4.2 Cumulative Distribution Functions 70

4.3 Mean and Variance of a Continuous Random Variable 71

4.4 Continuous Uniform Distribution 72

4.5 Normal Distribution 73

4.6 Normal Approximation to the Binomial and Poisson Distributions 79

4.7 Exponential Distribution 83

4.8 Erlang and Gamma Distributions 86

4.9 Weibull Distribution 89

4.10 Lognormal Distribution 90

4.11 Beta Distribution 92

5 Joint Probability Distributions 95

5.1 Joint Probability Distributions for Two Random Variables 96

5.2 Conditional Probability Distributions and Independence 102

5.3 Joint Probability Distributions for More Than Two Random Variables 107

5.4 Covariance and Correlation 110

5.5 Common Joint Distributions 113

5.5.1 Multinomial Probability Distribution 113

5.5.2 Bivariate Normal Distribution 115

5.6 Linear Functions of Random Variables 117

5.7 General Functions of Random Variables 120

5.8 Moment-Generating Functions 121

6 Descriptive Statistics 126

6.1 Numerical Summaries of Data 127

6.2 Stem-and-Leaf Diagrams 131

6.3 Frequency Distributions and Histograms 135

6.4 Box Plots 139

6.5 Time Sequence Plots 140

6.6 Scatter Diagrams 142

6.7 Probability Plots 144

7 Point Estimation of Parameters and Sampling Distributions 148

7.1 Point Estimation 149

7.2 Sampling Distributions and the Central Limit Theorem 150

7.3 General Concepts of Point Estimation 156

7.3.1 Unbiased Estimators 156

7.3.2 Variance of a Point Estimator 157

7.3.3 Standard Error: Reporting a Point Estimate 158

7.3.4 Bootstrap Standard Error 159

7.3.5 Mean Squared Error of an Estimator 160

7.4 Methods of Point Estimation 161

7.4.1 Method of Moments 162

7.4.2 Method of Maximum Likelihood 163

7.4.3 Bayesian Estimation of Parameters 167

8 Statistical Intervals for a Single Sample 170

8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known 172

...

Biographie:

1 The Role of Statistics in Engineering 1

1.1 The Engineering Method and Statistical Thinking 2

1.1.1 Variability 3

1.1.2 Populations and Samples 5

1.2 Collecting Engineering Data 5

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 Observing Processes over Time 9

1.3 Mechanistic and Empirical Models 12

1.4 Probability and Probability Models 15

2 Probability 17

2.1 Sample Spaces and Events 18

2.1.1 Random Experiments 18

2.1.2 Sample Spaces 19

2.1.3 Events 21

2.2 Counting Techniques 23

2.3 Interpretations and Axioms of Probability 26

2.4 Unions of Events and Addition Rules 29

2.5 Conditional Probability 31

2.6 Intersections of Events and Multiplication and Total Probability Rules 34

2.7 Independence 36

2.8 Bayes' Theorem 39

2.9 Random Variables 40

3 Discrete Random Variables and Probability Distributions 42

3.1 Probability Distributions and Probability Mass Functions 43

3.2 Cumulative Distribution Functions 45

3.3 Mean and Variance of a Discrete Random Variable 47

3.4 Discrete Uniform Distribution 49

3.5 Binomial Distribution 51

3.6 Geometric and Negative Binomial Distributions 55

3.7 Hypergeometric Distribution 59

3.8 Poisson Distribution 63

4 Continuous Random Variables and Probability Distributions 66

4.1 Probability Distributions and Probability Density Functions 67

4.2 Cumulative Distribution Functions 70

4.3 Mean and Variance of a Continuous Random Variable 71

4.4 Continuous Uniform Distribution 72

4.5 Normal Distribution 73

4.6 Normal Approximation to the Binomial and Poisson Distributions 79

4.7 Exponential Distribution 83

4.8 Erlang and Gamma Distributions 86

4.9 Weibull Distribution 89

4.10 Lognormal Distribution 90

4.11 Beta Distribution 92

5 Joint Probability Distributions 95

5.1 Joint Probability Distributions for Two Random Variables 96

5.2 Conditional Probability Distributions and Independence 102

5.3 Joint Probability Distributions for More Than Two Random Variables 107

5.4 Covariance and Correlation 110

5.5 Common Joint Distributions 113

5.5.1 Multinomial Probability Distribution 113

5.5.2 Bivariate Normal Distribution 115

5.6 Linear Functions of Random Variables 117

5.7 General Functions of Random Variables 120

5.8 Moment-Generating Functions 121

6 Descriptive Statistics 126

6.1 Numerical Summaries of Data 127

6.2 Stem-and-Leaf Diagrams 131

6.3 Frequency Distributions and Histograms 135

6.4 Box Plots 139

6.5 Time Sequence Plots 140

6.6 Scatter Diagrams 142

6.7 Probability Plots 144

7 Point Estimation of Parameters and Sampling Distributions 148

7.1 Point Estimation 149

7.2 Sampling Distributions and the Central Limit Theorem 150

7.3 General Concepts of Point Estimation 156

7.3.1 Unbiased Estimators 156

7.3.2 Variance of a Point Estimator 157

7.3.3 Standard Error: Reporting a Point Estimate 158

7.3.4 Bootstrap Standard Error 159

7.3.5 Mean Squared Error of an Estimator 160

7.4 Methods of Point Estimation 161

7.4.1 Method of Moments 162

7.4.2 Method of Maximum Likelihood 163

7.4.3 Bayesian Estimation of Parameters 167

8 Statistical Intervals for a Single Sample 170

8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known 172

...

Sommaire:

1 The Role of Statistics in Engineering 1

1.1 The Engineering Method and Statistical Thinking 2

1.1.1 Variability 3

1.1.2 Populations and Samples 5

1.2 Collecting Engineering Data 5

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 Observing Processes over Time 9

1.3 Mechanistic and Empirical Models 12

1.4 Probability and Probability Models 15

2 Probability 17

2.1 Sample Spaces and Events 18

2.1.1 Random Experiments 18

2.1.2 Sample Spaces 19

2.1.3 Events 21

2.2 Counting Techniques 23

2.3 Interpretations and Axioms of Probability 26

2.4 Unions of Events and Addition Rules 29

2.5 Conditional Probability 31

2.6 Intersections of Events and Multiplication and Total Probability Rules 34

2.7 Independence 36

2.8 Bayes' Theorem 39

2.9 Random Variables 40

3 Discrete Random Variables and Probability Distributions 42

3.1 Probability Distributions and Probability Mass Functions 43

3.2 Cumulative Distribution Functions 45

3.3 Mean and Variance of a Discrete Random Variable 47

3.4 Discrete Uniform Distribution 49

3.5 Binomial Distribution 51

3.6 Geometric and Negative Binomial Distributions 55

3.7 Hypergeometric Distribution 59

3.8 Poisson Distribution 63

4 Continuous Random Variables and Probability Distributions 66

4.1 Probability Distributions and Probability Density Functions 67

4.2 Cumulative Distribution Functions 70

4.3 Mean and Variance of a Continuous Random Variable 71

4.4 Continuous Uniform Distribution 72

4.5 Normal Distribution 73

4.6 Normal Approximation to the Binomial and Poisson Distributions 79

4.7 Exponential Distribution 83

4.8 Erlang and Gamma Distributions 86

4.9 Weibull Distribution 89

4.10 Lognormal Distribution 90

4.11 Beta Distribution 92

5 Joint Probability Distributions 95

5.1 Joint Probability Distributions for Two Random Variables 96

5.2 Conditional Probability Distributions and Independence 102

5.3 Joint Probability Distributions for More Than Two Random Variables 107

5.4 Covariance and Correlation 110

5.5 Common Joint Distributions 113

5.5.1 Multinomial Probability Distribution 113

5.5.2 Bivariate Normal Distribution 115

5.6 Linear Functions of Random Variables 117

5.7 General Functions of Random Variables 120

5.8 Moment-Generating Functions 121

6 Descriptive Statistics 126

6.1 Numerical Summaries of Data 127

6.2 Stem-and-Leaf Diagrams 131

6.3 Frequency Distributions and Histograms 135

6.4 Box Plots 139

6.5 Time Sequence Plots 140

6.6 Scatter Diagrams 142

6.7 Probability Plots 144

7 Point Estimation of Parameters and Sampling Distributions 148

7.1 Point Estimation 149

7.2 Sampling Distributions and the Central Limit Theorem 150

7.3 General Concepts of Point Estimation 156

7.3.1 Unbiased Estimators 156

7.3.2 Variance of a Point Estimator 157

7.3.3 Standard Error: Reporting a Point Estimate 158

7.3.4 Bootstrap Standard Error 159

7.3.5 Mean Squared Error of an Estimator 160

7.4 Methods of Point Estimation 161

7.4.1 Method of Moments 162

7.4.2 Method of Maximum Likelihood 163

7.4.3 Bayesian Estimation of Parameters 167

8 Statistical Intervals for a Single Sample 170

8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known 172

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