Probability and statistics in the engineering and computing sciences:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw Hill Book Comp.
1986
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 643 S. |
| ISBN: | 0070423512 |
Internformat
MARC
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| 245 | 1 | 0 | |a Probability and statistics in the engineering and computing sciences |c J. S. Milton ; Jesse C. Arnold |
| 264 | 1 | |a New York [u.a.] |b McGraw Hill Book Comp. |c 1986 | |
| 300 | |a XVI, 643 S. | ||
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Datensatz im Suchindex
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| adam_text | CONTENTS
Preface xiii
Chapter 1 Introduction to Probability and Counting 1
1.1 Interpreting Probabilities 2
1.2 Sample Spaces and Events 4
1.3 Permutations and Combinations 8
Counting Permutations 9
Counting Combinations 13
Chapter Summary 14
Exercises 15
Review Exercises 19
Chapter 2 Some Probability Laws 21
2.1 Axioms of Probability 21
The General Addition Rule 23
2.2 Conditional Probability 25
2.3 Independence and the Multiplication Rule 26
The Multiplication Rule 31
2.4 Bayes Theorem (Optional) 32
Chapter Summary 34
Exercises 34
Review Exercises 39
Chapter 3 Discrete Distributions 41
3.1 Random Variables 41
3.2 Discrete Densities 42
3.3 Expectation and Distribution Parameters 44
3.4 Moment Generating Function and the
Geometric Distribution 52
Geometric Distribution 52
Moment Generating Function 55
vii
viii contents
3.5 Binomial Distribution 59
3.6 Hypergeometric Distribution 63
3.7 Poisson Distribution 66
3.8 Simulating a Discrete Distribution (Optional) 72
Chapter Summary 74
Exercises 74
Review Exercises 86
Chapter 4 Continuous Distributions 88
4.1 Continuous Densities 88
4.2 Expectation and Distribution Parameters 94
4.3 Gamma Distribution 97
Exponential Distribution 100
Chi Square Distribution 102
4.4 Normal Distribution 103
4.5 Normal Approximations 109
4.6 Weibull Distribution and Reliability 112
Reliability 113
4.7 Simulating a Continuous Distribution (Optional) 116
Chapter Summary 118
Exercises 119
Review Exercises 133
Chapter 5 Joint Distributions 135
5.1 Joint Densities and Independence 135
Independence 142
5.2 Expectation and Co variance 143
5.3 Correlation 148
5.4 Conditional Densities and Regression 152
Chapter Summary 156
Exercises 157
Review Exercises 163
Chapter 6 Descriptive Statistics 165
6.1 Random Sampling 165
6.2 Picturing the Distribution 168
Stem and Leaf Charts 169
Histograms and Ogives 170
6.3 Sample Statistics 173
Chapter Summary 177
Exercises 178
Review Exercises 184
Computing Supplement 185
/ Summary Statistics and Histograms 185
CONTENTS ix
Chapter 7 Estimation 189
7.1 Point Estimation 189
7.2 The Method of Moments and Maximum Likelihood 192
Maximum Likelihood Estimators 194
7.3 Functions of Random Variables—Distribution of X 197
Distribution of X 200
7.4 Interval Estimation and the Central Limit Theorem 201
Chapter Summary 206
Exercises 207
Review Exercises 215
Chapter 8 Inferences on the Mean and Variance of
a Distribution 218
8.1 Interval Estimation of Variability 218
8.2 Estimating the Mean and the Student r Distribution 222
8.3 Hypothesis Testing 227
8.4 Significance Testing 231
8.5 Hypothesis and Significance Tests on the Mean 234
8.6 Testing for Normality and Hypothesis Tests on the Variance 237
Testing Hypotheses on the Variance 241
8.7 Alternative Nonparametric Methods 242
Sign Test for Median 243
Wilcoxon Signed Rank Test 245
ChapterSummary 247
Exercises 249
Review Exercises 266
Computing Supplement 267
// One Sample T Tests and Confidence Intervals 267
/// Testing for Normality 268
Chapter 9 Inferences on Proportions 271
9.1 Estimating Proportions 271
9.2 Testing Hypotheses on a Proportion 277
9.3 Comparing Two Proportions: Estimation 278
9.4 Comparing Two Proportions: Hypothesis Testing 282
Chapter Summary 285
Exercises 286
Review Exercises 292
Chapter 10 Comparing Two Means 295
10.1 Point Estimation: Independent Samples 295
10.2 Comparing Variances: The F Distribution 297
10.3 Comparing Means: Variances Equal 302
10.4 Comparing Means: Variances Unequal 307
10.5 Comparing Means: Paired Data 309
X CONTENTS
10.6 Alternative Nonparametric Methods 311
Wilcoxon Rank Sum Test 311
Wilcoxon Signed Rank Test for Paired Observations 313
Chapter Summary 315
Exercises 316
Review Exercises 331
Computing Supplement 333
IV Comparing Means and Variances 333
V Paired T Test 334
Chapter 11 Simple Linear Regression and Correlation 336
11.1 Model and Parameter Estimation 338
Description of Model 338
Least Squares Estimation 340
11.2 Properties of Least Squares Estimators 344
11.3 Confidence Interval Estimation and Hypothesis Testing 350
Inferences about Slope 351
Inferences about Intercept 354
Inferences about Predicted Mean 355
Inferences about Single Predicted Value 356
11.4 Repeated Measures and Lack of Fit 361
11.5 Correlation 364
Chapter Summary 371
Exercises 372
Review Exercises 379
Computing Supplement 382
VI Scattergrams, Estimation of fi0 and fily and Using the
Regression Line for Predictions 382
VII Testing Ho:Pl=0 386
VIII Confidence Intervals on po,puiiYlx,Y x 386
IX Testing for Lack of Fit 389
X Correlation 391
Chapter 12 Multiple Linear Regression Models 393
12.1 Least Squares Procedures for Model Fitting 393
Polynomial Model of Degree p 394
Multiple Linear Regression Model 398
12.2 A Matrix Approach to Least Squares 401
12.3 Properties of the Least Squares Estimators 409
12.4 Interval Estimation 415
Confidence Interval on a Single Slope 416
Confidence Interval on Predicted Mean 417
Confidence Interval on Single Predicted Response 418
12.5 Testing Hypotheses about Model Parameters 419
Testing a Single Predictor Variable 419
Testing for Significant Regression 420
Testing a Subset of Predictor Variables 422
CONTENTS XI
12.6 Criteria for Variable Selection 424
Forward Selection Method 424
Backward Elimination Procedure 425
Stepwise Method 426
Maximum R2 Method 428
Mallow s Ck Statistic 428
PRESS Statistic 429
12.7 Concluding Comments 435
Chapter Summary 435
Exercises 436
Review Exercises 443
Computing Supplement 444
XI Multiple Regression 444
XII Polynomial Regression 447
Chapter 13 Analysis of Variance 451
13.1 One Way Classification Fixed Effects Model 452
13.2 Comparing Variances 461
13.3 Multiple Comparisons 463
13.4 Randomized Complete Block Design 467
Paired Comparisons 474
13.5 Random Effects Models 476
One Way Classification 476
Randomized Complete Block 479
13.6 Factorial Experiments 480
Fixed Effects Model 480
Paired Comparisons 487
Random Effects Model 490
Mixed Effects Model 492
13.7 Design Models in Matrix Form 494
13.8 Alternative Nonparametric Methods 498
Kruskal Wallis Test 498
Friedman Test 500
Chapter Summary 501
Exercises 502
Review Exercises 510
Computing Supplement 513
XIII One Way Classification with Multiple Comparisons 513
XIV Randomized Complete Blocks with Multiple Comparisons 515
XV Two Way Classification with Multiple Comparisons 517
Chapter 14 Categorical Data 522
14.1 Multinomial Distribution 522
14.2 Chi Square Goodness of Fit Tests 524
Testing for Normality 526
14.3 Testing for Independence 531
r x c Test for Independence 536
Xli CONTENTS
14.4 Comparing Proportions 538
r x c Test for Homogeneity 541
Comparing Proportions with Paired Data 543
Chapter Summary 544
Exercises 545
Review Exercises 552
Chapter 15 Statistical Quality Control 555
15.1 X Charts and R Charts 556
Control Chart for the Sample Mean 556
Control Chart for the Sample Range 560
15.2 P Charts and C Charts 563
Control Chart for Proportion Defective 563
Control Chart for Average Number of Defects 566
15.3 Acceptance Sampling 566
Chapter Summary 571
Exercises 572
References 575
Appendix A Statistical Tables 577
/ Cumulative Binomial Distribution 579
// Cumulative Poisson Distribution 581
/// A Table of Random Digits 583
IV Cumulative Chi Square Distribution 585
V Cumulative Standard Normal Distribution 587
VI T Distribution 589
VII Sample Size for Estimating the Mean 590
VIII Wilcoxon Signed Rank Test 592
IX F Distribution 594
X Wilcoxon Rank Sum Test 602
XI Least Significant Studentized Ranges rp 606
XII Control Chart Constants 607
Appendix B Answers to Selected Problems 608
Index 639
|
| adam_txt |
CONTENTS
Preface xiii
Chapter 1 Introduction to Probability and Counting 1
1.1 Interpreting Probabilities 2
1.2 Sample Spaces and Events 4
1.3 Permutations and Combinations 8
Counting Permutations 9
Counting Combinations 13
Chapter Summary 14
Exercises 15
Review Exercises 19
Chapter 2 Some Probability Laws 21
2.1 Axioms of Probability 21
The General Addition Rule 23
2.2 Conditional Probability 25
2.3 Independence and the Multiplication Rule 26
The Multiplication Rule 31
2.4 Bayes Theorem (Optional) 32
Chapter Summary 34
Exercises 34
Review Exercises 39
Chapter 3 Discrete Distributions 41
3.1 Random Variables 41
3.2 Discrete Densities 42
3.3 Expectation and Distribution Parameters 44
3.4 Moment Generating Function and the
Geometric Distribution 52
Geometric Distribution 52
Moment Generating Function 55
vii
viii contents
3.5 Binomial Distribution 59
3.6 Hypergeometric Distribution 63
3.7 Poisson Distribution 66
3.8 Simulating a Discrete Distribution (Optional) 72
Chapter Summary 74
Exercises 74
Review Exercises 86
Chapter 4 Continuous Distributions 88
4.1 Continuous Densities 88
4.2 Expectation and Distribution Parameters 94
4.3 Gamma Distribution 97
Exponential Distribution 100
Chi Square Distribution 102
4.4 Normal Distribution 103
4.5 Normal Approximations 109
4.6 Weibull Distribution and Reliability 112
Reliability 113
4.7 Simulating a Continuous Distribution (Optional) 116
Chapter Summary 118
Exercises 119
Review Exercises 133
Chapter 5 Joint Distributions 135
5.1 Joint Densities and Independence 135
Independence 142
5.2 Expectation and Co variance 143
5.3 Correlation 148
5.4 Conditional Densities and Regression 152
Chapter Summary 156
Exercises 157
Review Exercises 163
Chapter 6 Descriptive Statistics 165
6.1 Random Sampling 165
6.2 Picturing the Distribution 168
Stem and Leaf Charts 169
Histograms and Ogives 170
6.3 Sample Statistics 173
Chapter Summary 177
Exercises 178
Review Exercises 184
Computing Supplement 185
/ Summary Statistics and Histograms 185
CONTENTS ix
Chapter 7 Estimation 189
7.1 Point Estimation 189
7.2 The Method of Moments and Maximum Likelihood 192
Maximum Likelihood Estimators 194
7.3 Functions of Random Variables—Distribution of X 197
Distribution of X 200
7.4 Interval Estimation and the Central Limit Theorem 201
Chapter Summary 206
Exercises 207
Review Exercises 215
Chapter 8 Inferences on the Mean and Variance of
a Distribution 218
8.1 Interval Estimation of Variability 218
8.2 Estimating the Mean and the Student r Distribution 222
8.3 Hypothesis Testing 227
8.4 Significance Testing 231
8.5 Hypothesis and Significance Tests on the Mean 234
8.6 Testing for Normality and Hypothesis Tests on the Variance 237
Testing Hypotheses on the Variance 241
8.7 Alternative Nonparametric Methods 242
Sign Test for Median 243
Wilcoxon Signed Rank Test 245
ChapterSummary 247
Exercises 249
Review Exercises 266
Computing Supplement 267
// One Sample T Tests and Confidence Intervals 267
/// Testing for Normality 268
Chapter 9 Inferences on Proportions 271
9.1 Estimating Proportions 271
9.2 Testing Hypotheses on a Proportion 277
9.3 Comparing Two Proportions: Estimation 278
9.4 Comparing Two Proportions: Hypothesis Testing 282
Chapter Summary 285
Exercises 286
Review Exercises 292
Chapter 10 Comparing Two Means 295
10.1 Point Estimation: Independent Samples 295
10.2 Comparing Variances: The F Distribution 297
10.3 Comparing Means: Variances Equal 302
10.4 Comparing Means: Variances Unequal 307
10.5 Comparing Means: Paired Data 309
X CONTENTS
10.6 Alternative Nonparametric Methods 311
Wilcoxon Rank Sum Test 311
Wilcoxon Signed Rank Test for Paired Observations 313
Chapter Summary 315
Exercises 316
Review Exercises 331
Computing Supplement 333
IV Comparing Means and Variances 333
V Paired T Test 334
Chapter 11 Simple Linear Regression and Correlation 336
11.1 Model and Parameter Estimation 338
Description of Model 338
Least Squares Estimation 340
11.2 Properties of Least Squares Estimators 344
11.3 Confidence Interval Estimation and Hypothesis Testing 350
Inferences about Slope 351
Inferences about Intercept 354
Inferences about Predicted Mean 355
Inferences about Single Predicted Value 356
11.4 Repeated Measures and Lack of Fit 361
11.5 Correlation 364
Chapter Summary 371
Exercises 372
Review Exercises 379
Computing Supplement 382
VI Scattergrams, Estimation of fi0 and fily and Using the
Regression Line for Predictions 382
VII Testing Ho:Pl=0 386
VIII Confidence Intervals on po,puiiYlx,Y\x 386
IX Testing for Lack of Fit 389
X Correlation 391
Chapter 12 Multiple Linear Regression Models 393
12.1 Least Squares Procedures for Model Fitting 393
Polynomial Model of Degree p 394
Multiple Linear Regression Model 398
12.2 A Matrix Approach to Least Squares 401
12.3 Properties of the Least Squares Estimators 409
12.4 Interval Estimation 415
Confidence Interval on a Single Slope 416
Confidence Interval on Predicted Mean 417
Confidence Interval on Single Predicted Response 418
12.5 Testing Hypotheses about Model Parameters 419
Testing a Single Predictor Variable 419
Testing for Significant Regression 420
Testing a Subset of Predictor Variables 422
CONTENTS XI
12.6 Criteria for Variable Selection 424
Forward Selection Method 424
Backward Elimination Procedure 425
Stepwise Method 426
Maximum R2 Method 428
Mallow's Ck Statistic 428
PRESS Statistic 429
12.7 Concluding Comments 435
Chapter Summary 435
Exercises 436
Review Exercises 443
Computing Supplement 444
XI Multiple Regression 444
XII Polynomial Regression 447
Chapter 13 Analysis of Variance 451
13.1 One Way Classification Fixed Effects Model 452
13.2 Comparing Variances 461
13.3 Multiple Comparisons 463
13.4 Randomized Complete Block Design 467
Paired Comparisons 474
13.5 Random Effects Models 476
One Way Classification 476
Randomized Complete Block 479
13.6 Factorial Experiments 480
Fixed Effects Model 480
Paired Comparisons 487
Random Effects Model 490
Mixed Effects Model 492
13.7 Design Models in Matrix Form 494
13.8 Alternative Nonparametric Methods 498
Kruskal Wallis Test 498
Friedman Test 500
Chapter Summary 501
Exercises 502
Review Exercises 510
Computing Supplement 513
XIII One Way Classification with Multiple Comparisons 513
XIV Randomized Complete Blocks with Multiple Comparisons 515
XV Two Way Classification with Multiple Comparisons 517
Chapter 14 Categorical Data 522
14.1 Multinomial Distribution 522
14.2 Chi Square Goodness of Fit Tests 524
Testing for Normality 526
14.3 Testing for Independence 531
r x c Test for Independence 536
Xli CONTENTS
14.4 Comparing Proportions 538
r x c Test for Homogeneity 541
Comparing Proportions with Paired Data 543
Chapter Summary 544
Exercises 545
Review Exercises 552
Chapter 15 Statistical Quality Control 555
15.1 X Charts and R Charts 556
Control Chart for the Sample Mean 556
Control Chart for the Sample Range 560
15.2 P Charts and C Charts 563
Control Chart for Proportion Defective 563
Control Chart for Average Number of Defects 566
15.3 Acceptance Sampling 566
Chapter Summary 571
Exercises 572
References 575
Appendix A Statistical Tables 577
/ Cumulative Binomial Distribution 579
// Cumulative Poisson Distribution 581
/// A Table of Random Digits 583
IV Cumulative Chi Square Distribution 585
V Cumulative Standard Normal Distribution 587
VI T Distribution 589
VII Sample Size for Estimating the Mean 590
VIII Wilcoxon Signed Rank Test 592
IX F Distribution 594
X Wilcoxon Rank Sum Test 602
XI Least Significant Studentized Ranges rp 606
XII Control Chart Constants 607
Appendix B Answers to Selected Problems 608
Index 639 |
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| index_date | 2024-07-02T16:03:20Z |
| indexdate | 2024-07-09T20:46:22Z |
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| isbn | 0070423512 |
| language | English |
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| spelling | Milton, Janet S. Verfasser aut Probability and statistics in the engineering and computing sciences J. S. Milton ; Jesse C. Arnold New York [u.a.] McGraw Hill Book Comp. 1986 XVI, 643 S. txt rdacontent n rdamedia nc rdacarrier Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Statistik (DE-588)4056995-0 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Arnold, Jesse C. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015085361&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Milton, Janet S. Arnold, Jesse C. Probability and statistics in the engineering and computing sciences Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4064324-4 (DE-588)4143389-0 |
| title | Probability and statistics in the engineering and computing sciences |
| title_auth | Probability and statistics in the engineering and computing sciences |
| title_exact_search | Probability and statistics in the engineering and computing sciences |
| title_exact_search_txtP | Probability and statistics in the engineering and computing sciences |
| title_full | Probability and statistics in the engineering and computing sciences J. S. Milton ; Jesse C. Arnold |
| title_fullStr | Probability and statistics in the engineering and computing sciences J. S. Milton ; Jesse C. Arnold |
| title_full_unstemmed | Probability and statistics in the engineering and computing sciences J. S. Milton ; Jesse C. Arnold |
| title_short | Probability and statistics in the engineering and computing sciences |
| title_sort | probability and statistics in the engineering and computing sciences |
| topic | Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Statistik Wahrscheinlichkeitsrechnung Aufgabensammlung |
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