Introduction to probability and statistics for engineers and scientists:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2009
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 664 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0123704839 9780123704832 |
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MARC
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| 100 | 1 | |a Ross, Sheldon M. |d 1943- |e Verfasser |0 (DE-588)123762235 |4 aut | |
| 245 | 1 | 0 | |a Introduction to probability and statistics for engineers and scientists |c Sheldon M. Ross |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2009 | |
| 300 | |a XV, 664 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Ingénierie - Méthodes statistiques | |
| 650 | 4 | |a Probabilités | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 4 | |a Mathematical statistics | |
| 650 | 4 | |a Probabilities | |
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Record in the Search Index
| _version_ | 1804139005264003072 |
|---|---|
| adam_text | Contents
Preface
хш
Chapter I Introduction to Statistics
................................... 1
1.1 Introduction
................................................. 1
1.2
Data Collection and Descriptive Statistics
......................... 1
1.3
Inferential Statistics and Probability Models
........................ 2
1.4
Populations and Samples
....................................... 3
1.5
A Brief History of Statistics
..................................... 3
Problems
.................................................... 7
Chapter
2
Descriptive Statistics
...................................... 9
2.1
Introduction
................................................. 9
2.2
Describing Data Sets
.......................................... 9
2.2.1
Frequency Tables and Graphs
................................. 10
2.2.2
Relative Frequency Tables and Graphs
........................... 10
2.2.3
Grouped Data, Histograms, Ogives, and Stem and Leaf Plots
.......... 14
23
Summarizing Data Sets
........................................ 17
2.3.1
Sample Mean, Sample Median, and Sample Mode
.................. 17
2.3.2
Sample Variance and Sample Standard Deviation
................... 22
2.3.3
Sample Percentiles and Box Plots
............................... 24
2.4
Chebyshev s Inequality
......................................... 27
2.5
Normal Data Sets
............................................. 31
2.6
Paired Data Sets and the Sample Correlation Coefficient
.............. 33
Problems
.................................................... 41
Chapter
3
Elements of Probability
.................................... 55
3.1
Introduction
................................................. 55
3.2
Sample Space and Events
....................................... 56
3.3
Venn Diagrams and the Algebra of Events
......................... 58
3.4
Axioms of Probability
.......................................... 59
VII
y¡¡¡ Contente
3.5
Sample Spaces Having Equally Likely Outcomes
.................... 61
3.6
Conditional Probability
........................................ 67
3.7
Bayes
Formula
............................................... 70
3.8
Independent Events
........................................... 76
Problems
.................................................... 80
Chapter
4
Random Variables and Expectation
......................... 89
4.1
Random Variables
............................................. 89
4.Î
Types of Random Variables
..................................... 92
4.3
Joindy Distributed Random Variables
............................. 95
4.3.1
Independent Random Variables
................................101
*4.3.2 Conditional Distributions
....................................105
4.4
Expectation
..................................................107
4.5
Properties of the Expected Value
.................................
Ill
4.5.1
Expected Value of Sums of Random Variables
.....................115
4.6
Variance
.....................................................118
4.7
Covariance and Variance of Sums of Random Variables
...............121
4.8
Moment Generating Functions
..................................125
4.9
Chebyshev s Inequality and the Weak Law of Large Numbers
..........127
Problems
....................................................130
Chapter
5
Special Random Variables
..................................141
5.1
The Bernoulli and Binomial Random Variables
.....................141
S.I.I Computing die Binomial Distribution Function
...................147
5.2
The
Poisson
Random Variable
...................................148
5.2.1
Computing the
Poisson
Distribution Function
.....................155
5.3
The Hypergeometric Random Variable
............................156
5.4
The Uniform Random Variable
..................................160
5.5
Normal Random Variables
......................................168
5.6
Exponential Random Variables
..................................176
*5.6.l The
Poisson
Process
........................................180
*5.7 The Gamma Distribution
......................................183
5.8
Distributions Arising from the Normal
............................186
S.Í.I
The Chi-Square Distribution
..................................186
5.8.2
The ¿-Distribution
.........................................190
5.8.3
The ^-Distribution
.........................................192
*5.9 The Logistics Distribution
......................................193
Problems
....................................................195
Chapter
6
Distributions of Sampling Statistics
.........................203
6.1
Introduction
.................................................203
6.2
The Sample Mean
.............................................204
Contents
6.3
The Central Limit Theorem
.....................................206
6.3.1
Approximate Distribution of the Sample Mean
....................212
6.3.2
How Large a Sample Is Needed?
...............................214
6.4
The Sample Variance
..........................................215
6.5
Sampling Distributions from a Normal Population
..................216
6.5.1
Distribution of the Sample Mean
...............................217
6.5.2
Joint Distribution ofX and S2
................................217
6.6
Sampling from a Finite Population
...............................219
Problems
....................................................223
Chapter
7
Parameter Estimation
.....................................231
7.1
Introduction
.................................................231
7.2
Maximum Likelihood Estimators
................................232
*7.2.l Estimating Life Distributions
.................................240
7.3
Interval Estimates
.............................................242
7.3.1
Confidence Interval for a Normal Mean When the Variance
Is Unknown
..............................................248
7.3.2
Confidence Intervals for the Variance of a Normal Distribution
........253
7.4
Estimating the Difference in Means of Two Normal Populations
.......255
7.5
Approximate Confidence Interval for the Mean of a Bernoulli Random
Variable
.....................................................262
*7.6 Confidence Interval of the Mean of the Exponential Distribution
......267
*7.7 Evaluating a Point Estimator
....................................268
*7.8 The
Bayes
Estimator
...........................................274
Problems
....................................................279
Chapter
8
Hypothesis Testing
........................................293
8.1
Introduction
.................................................294
8.2
Significance Levels
............................................294
8.3
Tests Concerning the Mean of a Normal Population
.................295
8.3.1
Case of Known Variance
.....................................295
8.3.2
Case of Unknown Variance: The
ŕ-Test
..........................307
8.4
Testing the Equality of Means of Two Normal Populations
............314
8.4.1
Case of Known Variances
....................................314
8.4.2
Case of Unknown Variances
..................................316
8.4.3
Case of Unknown and Unequal Variances
........................320
8.4.4
The Paired i-Test
..........................................321
8.5
Hypothesis Tests Concerning the Variance of a Normal Population
.....323
8.5.1
Testing for the Equality of Variances of Two Normal Populations
.......324
8.6
Hypothesis Tests in Bernoulli Populations
.........................325
8.6.1
Testing die Equality of Parameters in Two Bernoulli Populations
........329
Contenti
8.7
Tests Concerning the Mean of
a Poisson
Distribution
................332
8.7.1
Testing the Relationship Between Two
Poisson
Parameters
............333
Problems
....................................................336
Chapter
9
Regression
...............................................353
9.1
Introduction
.................................................353
9.2
Least Squares Estimators of the Regression Parameters
...............355
9.3
Distribution of the Estimators
...................................357
9.4
Statistical Inferences About the Regression Parameters
................363
9.4.1
Inferences Concerning
β
....................................364
9.4.2
Inferences Concerning a
.....................................372
9.4.3
Inferences Concerning the Mean Response a
+ ßm.................373
9.4.4
Prediction Interval of a Future Response
.........................375
9.4.5
Summary of Distributional Results
.............................377
9.5
The Coefficient of Determination and the Sample Correlation
Coefficient
...................................................378
9.6
Analysis of Residuals: Assessing the Model
.........................380
9.7
Transforming to Linearity
......................................383
9.8
Weighted Least Squares
........................................386
9.9
Polynomial Regression
.........................................393
*9.IO Multiple Linear Regression
.....................................396
9.10.1
Predicting Future Responses
..................................407
9.1
1 Logistic Regression Models for Binary Output Data
.................412
Problems
....................................................415
Chapter
10
Analysis of Variance
.......................................441
10.1
Introduction
.................................................441
10.2
An Overview
.................................................442
10.3
One-Way Analysis of Variance
...................................444
103.1
Multiple Comparisons of Sample Means
.........................452
10.3.2
One-Way Analysis of Variance with Unequal Sample Sizes
............454
10.4
Two-Factor Analysis of Variance: Introduction and Parameter
Estimation
...................................................456
10.5
Two-Factor Analysis of Variance: Testing Hypotheses
.................460
10.6
Two-Way Analysis of Variance with Interaction
.....................465
Problems
....................................................473
Chapter 11 Goodness of Fit Tests and Categorical Data Analysis
..........485
I I.I Introduction
.................................................435
1
1.2
Goodness of Fit Tests When All Parameters Are Specified
.............486
1
1.2.1
Determining the Critical Region by Simulation
....................492
1
1.3
Goodness of Fit Tests When Some Parameters Are Unspecified
.........495
Contents
11
.4
Tests of Independence in Contingency Tables
.......................497
11.5
Tests of Independence in Contingency Tables Having Fixed
Marginal Totals
...............................................501
*l
1.6
The Kolmogorov-Smimov Goodness of Fit Test for Continuous Data.
.. 506
Problems
....................................................510
Chapter
12
Nonparametric Hypothesis Tests
............................517
12.1
Introduction
.................................................517
12.2
The Sign Test
................................................517
12.3
The Signed Rank Test
..........................................521
12.4
The Two-Sample Problem
......................................527
*
1
2.4.
1 The Classical Approximation and Simulation
......................531
12.5
The Runs Test for Randomness
..................................535
Problems
....................................................539
Chapter
13
Quality Control
..........................................547
13.1
Introduction
.................................................547
13.2
Control Charts for Average Values: The
Х
-Control Chart
.............548
13.2.1
Case of Unknown
μ
and
σ
...................................551
13.3
5-Control Charts
.............................................556
13.4
Control Charts for the Fraction Defective
.........................559
13.5
Control Charts for Number of Defects
............................561
13.6
Other Control Charts for Detecting Changes in the Population Mean
... 565
13.6.1
Moving-Average Control Charts
...............................565
13.6.2
Exponentially Weighted Moving-Average Control Charts
.............567
13.6.3
Cumulative Sum Control Charts
...............................573
Problems
....................................................575
Chapter
14*
Life Testing
..............................................583
14.1
Introduction
.................................................583
14.2
Hazard Rate Functions
.........................................583
14.3
The Exponential Distribution in Life Testing
.......................586
14.3.1
Simultaneous Testing
—
Stopping at the rth Failure
.................586
14.3.2
Sequential Testing
..........................................592
14.3.3
Simultaneous Testing
—
Stopping by a Fixed Time
..................596
14.3.4
The Bayesian Approach
......................................598
14.4
ATwo-Sample Problem
........................................600
14.5
The Weibull Distribution in Life Testing
..........................602
14.5.1
Parameter Estimation by Least Squares
...........................604
Problems
....................................................606
x¡¡
Contents
Chapter
15
Simulation, Bootstrap Statistical Methods, and
Permutation Tests
.........................................613
15.1
Introduction
.................................................613
15.2
Random Numbers
............................................614
15.2.1
The Monte Carlo Simulation Approach
..........................616
15.3
The Bootstrap Method
.........................................617
15.4
Permutation Tests
.............................................624
15.4.1
Normal Approximations in Permutation Tests
.....................627
15.4.2
Two-Sample Permutation Tests
................................631
15.5
Generating Discrete Random Variables
............................632
15.6
Generating Continuous Random Variables
.........................634
15.6.1
Generating a Normal Random Variable
..........................636
15.7
Determining the Number of Simulation Runs in a Monte Carlo Study
.. 637
Problems
....................................................638
Appendix of Tables
.....................................................641
Index
..............................................................647
*
Denotes optional material.
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 4. ed. |
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| id | DE-604.BV023805600 |
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| indexdate | 2024-07-09T21:37:12Z |
| institution | BVB |
| isbn | 0123704839 9780123704832 |
| language | English |
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| spelling | Ross, Sheldon M. 1943- Verfasser (DE-588)123762235 aut Introduction to probability and statistics for engineers and scientists Sheldon M. Ross 4. ed. Amsterdam [u.a.] Elsevier 2009 XV, 664 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Ingénierie - Méthodes statistiques Probabilités Statistique mathématique Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Statistik (DE-588)4056995-0 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017447775&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ross, Sheldon M. 1943- Introduction to probability and statistics for engineers and scientists Ingénierie - Méthodes statistiques Probabilités Statistique mathématique Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4064324-4 (DE-588)4123623-3 |
| title | Introduction to probability and statistics for engineers and scientists |
| title_auth | Introduction to probability and statistics for engineers and scientists |
| title_exact_search | Introduction to probability and statistics for engineers and scientists |
| title_full | Introduction to probability and statistics for engineers and scientists Sheldon M. Ross |
| title_fullStr | Introduction to probability and statistics for engineers and scientists Sheldon M. Ross |
| title_full_unstemmed | Introduction to probability and statistics for engineers and scientists Sheldon M. Ross |
| title_short | Introduction to probability and statistics for engineers and scientists |
| title_sort | introduction to probability and statistics for engineers and scientists |
| topic | Ingénierie - Méthodes statistiques Probabilités Statistique mathématique Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Ingénierie - Méthodes statistiques Probabilités Statistique mathématique Mathematical statistics Probabilities Statistik Wahrscheinlichkeitsrechnung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017447775&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rosssheldonm introductiontoprobabilityandstatisticsforengineersandscientists |