Introduction to probability and statistics for science, engineering, and finance:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "A Chapman & Hall book." Includes bibliographical references and index |
| Physical Description: | 667 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 1584888121 9781584888123 |
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| 020 | |a 9781584888123 |c alk. paper |9 978-1-58488-812-3 | ||
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| 084 | |a MAT 620f |2 stub | ||
| 084 | |a MAT 600f |2 stub | ||
| 100 | 1 | |a Rosenkrantz, Walter A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to probability and statistics for science, engineering, and finance |c Walter A. Rosenkrantz |
| 246 | 1 | 3 | |a Probability and statistics for science, engineering, and finance |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
| 300 | |a 667 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a "A Chapman & Hall book." | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Mathematical statistics | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsrechnung |0 (DE-588)4064324-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Statistik |0 (DE-588)4056995-0 |D s |
| 689 | 0 | |5 DE-604 | |
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| adam_text | Contents
Data
Analysis I
1.1
Orientation
.................................... 1
1.2
The Role and Scope of Statistics
in Science and Engineering ........ 2
1.3
Types of Data: Examples from Engineering, Public Health, and Finance
. 5
1.3.1
Univariate Data
............................. 5
1.3.2
Multivariate Data
............................ 7
1.3.3
Financial Data: Stock Market Prices and Their Time Series
..... 9
1.3.4
Stock Market Returns: Definition and Examples
........... 13
1.4
The Frequency Distribution of a Variable Defined on a Population
..... 17
1.4.1
Organizing the Data
........................... 17
1.4.2
Graphical Displays
............................ 18
1.4.3
Histograms
................................ 22
1.5
Quantiles of a Distribution
........................... 26
1.5.1
The Median
................................ 26
1.5.2
Quantiles of the Empirical Distribution Function
........... 27
1.6
Measures of Location (Central Value) and Variability
............ 32
1.6.1
The Sample Mean
............................ 32
1.6.2
Sample Standard Deviation: A Measure of Risk
............ 33
1.6.3
Mean-Standard Deviation Diagram of a Portfolio
........... 36
1.6.4
Linear Transformations of Data
..................... 37
1.7
Covariance, Correlation, and Regression: Computing a Stock s Beta
.... 38
1.7.1
Fitting a Straight Line to Bivariate Data
............... 40
1.8
Mathematical Details and Derivations
..................... 43
1.9
Chapter Summary
................................ 44
1.10
Problems
..................................... 44
1.11
Large Data Sets
................................. 65
1.12
To Probe Further
................................ 70
Probability Theory
71
2.1
Orientation
.................................... 71
2.2
Sample Space, Events, Axioms of Probability Theory
............ 72
2.2.1
Probability Measures
........................... 78
2.3
Mathematical Models of Random Sampling
.................. 84
2.3.1
Multinomial Coefficients
......................... 93
2.4
Conditional Probability and
Bayes
Theorem
................. 94
2.4.1
Conditional Probability
......................... 94
2.4.2
Bayes
Theorem
............................. 97
2.4.3
Independence
............................... 99
2.5
The Binomial Theorem
............................. 100
2.6
Chapter Summary
................................ 101
2.7
Problems
..................................... 101
2.8
To Probe Further
................................
Ill
Discrete Random Variables and Their Distribution Functions
113
3.1
Orientation
.................................... 113
3.2
Discrete Random Variables
........................... 114
3.2.1
Functions of a Random Variable
.................... 120
3.3
Expected Value and Variance of a Random Variable
............. 121
3.3.1
Moments of a Random Variable
..................... 125
3.3.2
Variance of a Random Variable
..................... 128
3.3.3
Chebyshev s Inequality
.......................... 130
3.4
The Hypergeometric Distribution
....................... 130
3.5
The Binomial Distribution
........................... 134
3.5.1
A Coin Tossing Model for Stock Market Returns
........... 140
3.6
The
Poisson
Distribution
............................ 144
3.7
Moment Generating Function: Discrete Random Variables
......... 146
3.8
Mathematical Details and Derivations
..................... 148
3.9
Chapter Summary
................................ 150
3.10
Problems
..................................... 151
3.11
To Probe Further
................................ 160
Continuous Random Variables and Their Distribution Functions
161
4.1
Orientation
.................................... 161
4.2
Random Variables with Continuous Distribution Functions: Definition and
Examples
..................................... 162
4.3
Expected Value. Moments, and Variance of a Continuous Random Variable
167
4.4
Moment Generating Function: Continuous Random Variables
....... 171
4.5
The Normal Distribution: Definition and Basic Properties
......... 172
4.6
The
Lognormal
Distribution: A Model for the Distribution of Stock Prices
177
4.7
The Normal Approximation to the Binomial Distribution
.......... 179
4.7.1
Distribution of the Sample Proportion
ρ
................ 185
4.8
Other Important Continuous Distributions
.................. 185
4.8.1
The Gamma and Chi-Square Distributions
.............. 185
4.8.2
The Weibull Distribution
........................ 188
4.8.3
The Beta Distribution
.......................... 188
4.9
Functions of a Random Variable
........................ 189
4.10
Mathematical Details and Derivations
..................... 191
4.11
Chapter Summary
................................ 192
4.12
Problems
..................................... 192
4.13
To Probe Further
................................ 202
Multivariate Probability Distributions
205
5.1
Orientation
.................................... 205
5.2
The Joint Distribution Function: Discrete Random Variables
........ 206
5.2.1
Independent Random Variables
..................... 211
5.3
The Multinomial Distribution
......................... 212
5.4
Mean and Variance of a Sum of Random Variables
.............. 213
5.4.1
The Law of Large Numbers for Sums of Independent and Identically
Distributed (iid) Random Variables
.................. 220
5.4.2
The Central Limit Theorem
....................... 222
5.5
Why Stock Prices Have
a
Lognormal
Distribution: An Application of the
Central Limit Theorem
............................. 224
5.5.1
The Binomial Lattice Model as an Approximation to a Continuous
Time Model for Stock Market Prices
.................. 227
5.6
Modern Portfolio
Theory ............................
230
5.6.1
Mean-Variance Analysis
of
a
Portfolio
................. 230
5.7
Risk Free and Risky Investing
......................... 232
5.7.1
Present Value Analysis of Risk Free and Risky Returns
....... 232
5.7.2
Present Value Analysis of Deterministic and Random Cash Flows
. . 235
5.8
Theory of Single and Multi-Period Binomial Options
............ 237
5.8.1
Black-Scholes Option Pricing Formula: Binomial Lattice Model
. . . 237
5.9
Black-Scholes Formula for Multi-Period Binomial Options
.......... 240
5.9.1
Black-Scholes Pricing Formula for Stock Prices Governed by a Log-
normal Distribution
........................... 242
5.10
The
Poisson
Process
............................... 243
5.10.1
The
Poisson
Process and the Gamma Distribution
.......... 246
5.11
Applications of Bernoulli Random Variables to Reliability Theory
..... 248
5.12
The Joint Distribution Function: Continuous Random Variables
...... 251
5.12.1
Functions of Random Vectors
...................... 254
5.12.2
Conditional Distributions and Conditional Expectations: Continuous
Case
.................................... 256
5.12.3
The
Divariate
Normal Distribution
................... 257
5.13
Mathematical Details and Derivations
..................... 258
5.14
Chapter Summary
................................ 263
5.15
Problems
..................................... 263
5.16
To Probe Further
................................ 275
Sampling Distribution Theory
277
6.1
Orientation
.................................... 277
6.2
Sampling from a Normal Distribution
..................... 277
6.3
The Distribution of the Sample Variance
................... 282
6.3.1
Student s
t
Distribution
......................... 284
6.3.2
The
F
Distribution
............................ 285
6.4
Mathematical Details and Derivations
..................... 286
6.5
Chapter Summary
................................ 287
6.6
Problems
..................................... 287
6.7
To Probe Further
................................ 290
Point and Interval Estimation
291
7.1
Orientation
.................................... 291
7.2
Estimating Population Parameters: Methods and Examples
......... 292
7.2.1
Some Properties of Estimators: Bias, Variance, and Consistency
. . 294
7.3
Confidence Intervals for the Mean and Variance
............... 296
7.3.1
Confidence Intervals for the Mean of a Normal Distribution: Variance
Unknown
................................. 299
7.3.2
Confidence Intervals for the Mean of an Arbitrary Distribution
. . . 300
7.3.3
Confidence Intervals for the Variance of a Normal Distribution
. . . 302
7.3.4
Value at Risk (VaR): An Application of Confidence Intervals to Risk
Management
............................... 303
7.4
Point and Interval Estimation for the Difference of Two Means
....... 304
7.4.1
Paired Samples
.............................. 305
7.5
Point and Interval Estimation for a Population Proportion
......... 307
7.5.1
Confidence Intervals for pi
—
p2
..................... 309
7.6
Some Methods of Estimation
.......................... 310
7.6.1
Method of Moments
........................... 310
7.6.2
Maximum
Likelihood Estimators
.................... 312
7.7
Chapter Summary
................................ 316
7.8
Problems
..................................... 316
7.9
To Probe Further
................................ 324
8
Hypothesis Testing
325
8.1
Orientation
.................................... 325
8.2
Tests of Statistical Hypotheses: Basic Concepts and Examples
....... 326
8.2.1
Significance Testing
........................... 336
8.2.2
Power Function and Sample Size
.................... 338
8.2.3
Large Sample Tests Concerning the Mean of an Arbitrary Distribution
339
8.2.4
Tests Concerning the Mean of a Distribution with Unknown Variance
340
8.3
Comparing Two Populations
.......................... 344
8.3.1
The Wilcoxon Rank Sum Test for Two Independent Samples
.... 347
8.3.2
A Test of the Equality of Two Variances
................ 350
8.4
Normal Probability Plots
............................ 351
8.5
Tests Concerning the Parameter
ρ
of a Binomial Distribution
........ 355
8.5.1
Tests of Hypotheses Concerning Two Binomial Distributions: Large
Sample Size
................................ 359
8.6
Chapter Summary
................................ 360
8.7
Problems
..................................... 361
8.8
To Probe Further
................................ 372
9
Statistical Analysis of Categorical Data
373
9.1
Orientation
.................................... 373
9.2
Chi-Square Tests
................................. 373
9.2.1
Chi-Square Tests When the Cell Probabilities Are Not Completely
Specified
.................................. 376
9.3
Contingency Tables
............................... 377
9.4
Chapter Summary
................................ 383
9.5
Problems
..................................... 383
9.6
To Probe Further
................................ 388
10
Linear Regression and Correlation
389
10.1
Orientation
.................................... 389
10.2
Method of Least Squares
............................ 390
10.2.1
Fitting a Straight Line via Ordinary Least Squares
.......... 392
10.3
The Simple Linear Regression Model
..................... 398
10.3.1
The Sampling Distribution of
/Зі,/Зо,
SSE, and
SSR
......... 399
10.3.2
Tests of Hypotheses Concerning the Regression Parameters
..... 402
10.3.3
Confidence Intervals and Prediction Intervals
............. 403
10.3.4
Displaying the Output of a Regression Analysis in an ANOVA Table
406
10.3.5
Curvilinear Regression
.......................... 408
10.4
Model Checking
................................. 411
10.5
Correlation Analysis
............................... 416
10.5.1
Computing the Market Risk of a Stock
................. 417
10.5.2
The Shapiro-Wilk Test for Normality
................. 421
10.6
Mathematical Details and Derivations
..................... 422
10.7
Chapter Summary
................................ 426
10.8
Problems
..................................... 426
10.9
Large Data Sets
................................. 437
10.10
To Probe Further
................................ 439
11
Multiple Linear Regression
441
11.1
Orientation
.................................... 441
11.2
The Matrix Approach to Simple Linear Regression
.............. 442
11.2.1
Sampling Distribution of the Least Squares Estimators
........ 447
11.2.2
Geometric Interpretation of the Least Squares Solution
....... 449
11.3
The Matrix Approach to Multiple Linear Regression
............. 450
11.3.1
Normal Equations. Fitted Values, and ANOVA Table for the Multiple
Linear Regression Model
......................... 454
11.3.2
Testing Hypotheses about the Regression Model
........... 457
11.3.3
Model Checking
............................. 460
11.3.4
Confidence Intervals and Prediction Intervals in Multiple Linear Re¬
gression
.................................. 462
11.4
Mathematical Details and Derivations
..................... 464
11.5
Chapter Summary
................................ 464
11.6
Problems
..................................... 465
11.7
To Probe Further
................................ 468
12
Single Factor Experiments: Analysis of Variance
469
12.1
Orientation
.................................... 469
12.2
The Single Factor ANOVA Model
....................... 469
12.2.1
Estimating the ANOVA Model Parameters
.............. 473
12.2.2
Testing Hypotheses about the Parameters
............... 475
12.2.3
Model Checking via Residual Plots
................... 478
12.2.4
Unequal Sample Sizes
.......................... 480
12.3
Confidence Intervals for the Treatment Means: Contrasts
.......... 482
12.3.1
Multiple Comparisons of Treatment Means
.............. 485
12.4
Random Effects Model
............................. 487
12.5
Mathematical Derivations and Details
..................... 489
12.6
Chapter Summary
................................ 490
12.7
Problems
..................................... 490
12.8
To Probe Further
................................ 496
13
Design and Analysis of Multi-Factor Experiments
497
13.1
Orientation
.................................... 497
13.2
Randomized Complete Block Designs
..................... 498
13.2.1
Confidence Intervals and Multiple Comparison Procedures
...... 507
13.2.2
Model Checking via Residual Plots
................... 508
13.3
Two Factor Experiments with
η
> 1
Observations per Cell
......... 508
13.3.1
Confidence Intervals and Multiple Comparisons
........... 520
13.4
2fc Factorial Designs
............................... 522
13.5
Chapter Summary
................................ 540
13.6
Problems
..................................... 540
13.7
To Probe Further
................................ 548
14
Statistical Quality Control
551
14.1
Orientation
.................................... 551
14.2
χ
and
R
Control Charts
............................. 552
14.2.1
Detecting a Shift in the Process Mean
................. 557
14.3
p
Charts and
с
Charts
.............................. 559
14.4
Chapter Summary
................................ 562
14.5
Problems
. . . .*................................. 562
14.6
To Probe Further
................................ 565
A Tables
567
A.I Cumulative Binomial Distribution
....................... 568
A.
2
Cumulative
Poisson
Distribution
........................ 570
A.3 Standard Normal Probabilities
......................... 572
A.
4
Critical Values tu(a) of the
t
Distribution
................... 574
A.5 Quantiles Qu(p)
=
χΙ(1 -ρ)
of the
χ2
Distribution
............. 575
A.6 Critical Values of the FVl
,„2
(α)
Distribution
................. 576
A.
7
Critical Values of the Studentized Range q(a; n^v)
.............. 580
A.8 Factors for Estimating
σ,
5,
or
ацмѕ
and
ац
from
R
............ 584
A.9 Factors for Determining from
R
the Three-Sigma Control Limits for X and
R
Charts
.................................„ . . 585
A.
10
Factors for Determining from
σ
the Three-Sigma Control Limits for X, R,
and
s
or
σ
амѕ
Charts
............................. 586
Answers to Selected Odd-Numbered Problems
589
1
Data Analysis
591
2
Probability Theory
597
3
Discrete Random. Variables and Their Distribution Functions
601
4
Continuous Random Variables and Their Distribution Functions
609
5
Multivariate Probability Distributions
617
6
Sampling Distribution Theory
623
7
Point and Interval Estimation
625
8
Hypothesis Testing
631
9
Statistical Analysis of Categorical Data
637
10
Linear Regression and Correlation
641
11
Multiple Linear Regression
645
12
Single Factor Experiments: Analysis of Variance
647
13
Design and Analysis of Multi-Factor Experiments
653
14
Statistical Quality Control
659
Index
661
|
| adam_txt |
Contents
Data
Analysis I
1.1
Orientation
. 1
1.2
The Role and Scope of Statistics
in Science and Engineering . 2
1.3
Types of Data: Examples from Engineering, Public Health, and Finance
. 5
1.3.1
Univariate Data
. 5
1.3.2
Multivariate Data
. 7
1.3.3
Financial Data: Stock Market Prices and Their Time Series
. 9
1.3.4
Stock Market Returns: Definition and Examples
. 13
1.4
The Frequency Distribution of a Variable Defined on a Population
. 17
1.4.1
Organizing the Data
. 17
1.4.2
Graphical Displays
. 18
1.4.3
Histograms
. 22
1.5
Quantiles of a Distribution
. 26
1.5.1
The Median
. 26
1.5.2
Quantiles of the Empirical Distribution Function
. 27
1.6
Measures of Location (Central Value) and Variability
. 32
1.6.1
The Sample Mean
. 32
1.6.2
Sample Standard Deviation: A Measure of Risk
. 33
1.6.3
Mean-Standard Deviation Diagram of a Portfolio
. 36
1.6.4
Linear Transformations of Data
. 37
1.7
Covariance, Correlation, and Regression: Computing a Stock's Beta
. 38
1.7.1
Fitting a Straight Line to Bivariate Data
. 40
1.8
Mathematical Details and Derivations
. 43
1.9
Chapter Summary
. 44
1.10
Problems
. 44
1.11
Large Data Sets
. 65
1.12
To Probe Further
. 70
Probability Theory
71
2.1
Orientation
. 71
2.2
Sample Space, Events, Axioms of Probability Theory
. 72
2.2.1
Probability Measures
. 78
2.3
Mathematical Models of Random Sampling
. 84
2.3.1
Multinomial Coefficients
. 93
2.4
Conditional Probability and
Bayes'
Theorem
. 94
2.4.1
Conditional Probability
. 94
2.4.2
Bayes'
Theorem
. 97
2.4.3
Independence
. 99
2.5
The Binomial Theorem
. 100
2.6
Chapter Summary
. 101
2.7
Problems
. 101
2.8
To Probe Further
.
Ill
Discrete Random Variables and Their Distribution Functions
113
3.1
Orientation
. 113
3.2
Discrete Random Variables
. 114
3.2.1
Functions of a Random Variable
. 120
3.3
Expected Value and Variance of a Random Variable
. 121
3.3.1
Moments of a Random Variable
. 125
3.3.2
Variance of a Random Variable
. 128
3.3.3
Chebyshev's Inequality
. 130
3.4
The Hypergeometric Distribution
. 130
3.5
The Binomial Distribution
. 134
3.5.1
A Coin Tossing Model for Stock Market Returns
. 140
3.6
The
Poisson
Distribution
. 144
3.7
Moment Generating Function: Discrete Random Variables
. 146
3.8
Mathematical Details and Derivations
. 148
3.9
Chapter Summary
. 150
3.10
Problems
. 151
3.11
To Probe Further
. 160
Continuous Random Variables and Their Distribution Functions
161
4.1
Orientation
. 161
4.2
Random Variables with Continuous Distribution Functions: Definition and
Examples
. 162
4.3
Expected Value. Moments, and Variance of a Continuous Random Variable
167
4.4
Moment Generating Function: Continuous Random Variables
. 171
4.5
The Normal Distribution: Definition and Basic Properties
. 172
4.6
The
Lognormal
Distribution: A Model for the Distribution of Stock Prices
177
4.7
The Normal Approximation to the Binomial Distribution
. 179
4.7.1
Distribution of the Sample Proportion
ρ
. 185
4.8
Other Important Continuous Distributions
. 185
4.8.1
The Gamma and Chi-Square Distributions
. 185
4.8.2
The Weibull Distribution
. 188
4.8.3
The Beta Distribution
. 188
4.9
Functions of a Random Variable
. 189
4.10
Mathematical Details and Derivations
. 191
4.11
Chapter Summary
. 192
4.12
Problems
. 192
4.13
To Probe Further
. 202
Multivariate Probability Distributions
205
5.1
Orientation
. 205
5.2
The Joint Distribution Function: Discrete Random Variables
. 206
5.2.1
Independent Random Variables
. 211
5.3
The Multinomial Distribution
. 212
5.4
Mean and Variance of a Sum of Random Variables
. 213
5.4.1
The Law of Large Numbers for Sums of Independent and Identically
Distributed (iid) Random Variables
. 220
5.4.2
The Central Limit Theorem
. 222
5.5
Why Stock Prices Have
a
Lognormal
Distribution: An Application of the
Central Limit Theorem
. 224
5.5.1
The Binomial Lattice Model as an Approximation to a Continuous
Time Model for Stock Market Prices
. 227
5.6
Modern Portfolio
Theory .
230
5.6.1
Mean-Variance Analysis
of
a
Portfolio
. 230
5.7
Risk Free and Risky Investing
. 232
5.7.1
Present Value Analysis of Risk Free and Risky Returns
. 232
5.7.2
Present Value Analysis of Deterministic and Random Cash Flows
. . 235
5.8
Theory of Single and Multi-Period Binomial Options
. 237
5.8.1
Black-Scholes Option Pricing Formula: Binomial Lattice Model
. . . 237
5.9
Black-Scholes Formula for Multi-Period Binomial Options
. 240
5.9.1
Black-Scholes Pricing Formula for Stock Prices Governed by a Log-
normal Distribution
. 242
5.10
The
Poisson
Process
. 243
5.10.1
The
Poisson
Process and the Gamma Distribution
. 246
5.11
Applications of Bernoulli Random Variables to Reliability Theory
. 248
5.12
The Joint Distribution Function: Continuous Random Variables
. 251
5.12.1
Functions of Random Vectors
. 254
5.12.2
Conditional Distributions and Conditional Expectations: Continuous
Case
. 256
5.12.3
The
Divariate
Normal Distribution
. 257
5.13
Mathematical Details and Derivations
. 258
5.14
Chapter Summary
. 263
5.15
Problems
. 263
5.16
To Probe Further
. 275
Sampling Distribution Theory
277
6.1
Orientation
. 277
6.2
Sampling from a Normal Distribution
. 277
6.3
The Distribution of the Sample Variance
. 282
6.3.1
Student's
t
Distribution
. 284
6.3.2
The
F
Distribution
. 285
6.4
Mathematical Details and Derivations
. 286
6.5
Chapter Summary
. 287
6.6
Problems
. 287
6.7
To Probe Further
. 290
Point and Interval Estimation
291
7.1
Orientation
. 291
7.2
Estimating Population Parameters: Methods and Examples
. 292
7.2.1
Some Properties of Estimators: Bias, Variance, and Consistency
. . 294
7.3
Confidence Intervals for the Mean and Variance
. 296
7.3.1
Confidence Intervals for the Mean of a Normal Distribution: Variance
Unknown
. 299
7.3.2
Confidence Intervals for the Mean of an Arbitrary Distribution
. . . 300
7.3.3
Confidence Intervals for the Variance of a Normal Distribution
. . . 302
7.3.4
Value at Risk (VaR): An Application of Confidence Intervals to Risk
Management
. 303
7.4
Point and Interval Estimation for the Difference of Two Means
. 304
7.4.1
Paired Samples
. 305
7.5
Point and Interval Estimation for a Population Proportion
. 307
7.5.1
Confidence Intervals for pi
—
p2
. 309
7.6
Some Methods of Estimation
. 310
7.6.1
Method of Moments
. 310
7.6.2
Maximum
Likelihood Estimators
. 312
7.7
Chapter Summary
. 316
7.8
Problems
. 316
7.9
To Probe Further
. 324
8
Hypothesis Testing
325
8.1
Orientation
. 325
8.2
Tests of Statistical Hypotheses: Basic Concepts and Examples
. 326
8.2.1
Significance Testing
. 336
8.2.2
Power Function and Sample Size
. 338
8.2.3
Large Sample Tests Concerning the Mean of an Arbitrary Distribution
339
8.2.4
Tests Concerning the Mean of a Distribution with Unknown Variance
340
8.3
Comparing Two Populations
. 344
8.3.1
The Wilcoxon Rank Sum Test for Two Independent Samples
. 347
8.3.2
A Test of the Equality of Two Variances
. 350
8.4
Normal Probability Plots
. 351
8.5
Tests Concerning the Parameter
ρ
of a Binomial Distribution
. 355
8.5.1
Tests of Hypotheses Concerning Two Binomial Distributions: Large
Sample Size
. 359
8.6
Chapter Summary
. 360
8.7
Problems
. 361
8.8
To Probe Further
. 372
9
Statistical Analysis of Categorical Data
373
9.1
Orientation
. 373
9.2
Chi-Square Tests
. 373
9.2.1
Chi-Square Tests When the Cell Probabilities Are Not Completely
Specified
. 376
9.3
Contingency Tables
. 377
9.4
Chapter Summary
. 383
9.5
Problems
. 383
9.6
To Probe Further
. 388
10
Linear Regression and Correlation
389
10.1
Orientation
. 389
10.2
Method of Least Squares
. 390
10.2.1
Fitting a Straight Line via Ordinary Least Squares
. 392
10.3
The Simple Linear Regression Model
. 398
10.3.1
The Sampling Distribution of
/Зі,/Зо,
SSE, and
SSR
. 399
10.3.2
Tests of Hypotheses Concerning the Regression Parameters
. 402
10.3.3
Confidence Intervals and Prediction Intervals
. 403
10.3.4
Displaying the Output of a Regression Analysis in an ANOVA Table
406
10.3.5
Curvilinear Regression
. 408
10.4
Model Checking
. 411
10.5
Correlation Analysis
. 416
10.5.1
Computing the Market Risk of a Stock
. 417
10.5.2
The Shapiro-Wilk Test for Normality
. 421
10.6
Mathematical Details and Derivations
. 422
10.7
Chapter Summary
. 426
10.8
Problems
. 426
10.9
Large Data Sets
. 437
10.10
To Probe Further
. 439
11
Multiple Linear Regression
441
11.1
Orientation
. 441
11.2
The Matrix Approach to Simple Linear Regression
. 442
11.2.1
Sampling Distribution of the Least Squares Estimators
. 447
11.2.2
Geometric Interpretation of the Least Squares Solution
. 449
11.3
The Matrix Approach to Multiple Linear Regression
. 450
11.3.1
Normal Equations. Fitted Values, and ANOVA Table for the Multiple
Linear Regression Model
. 454
11.3.2
Testing Hypotheses about the Regression Model
. 457
11.3.3
Model Checking
. 460
11.3.4
Confidence Intervals and Prediction Intervals in Multiple Linear Re¬
gression
. 462
11.4
Mathematical Details and Derivations
. 464
11.5
Chapter Summary
. 464
11.6
Problems
. 465
11.7
To Probe Further
. 468
12
Single Factor Experiments: Analysis of Variance
469
12.1
Orientation
. 469
12.2
The Single Factor ANOVA Model
. 469
12.2.1
Estimating the ANOVA Model Parameters
. 473
12.2.2
Testing Hypotheses about the Parameters
. 475
12.2.3
Model Checking via Residual Plots
. 478
12.2.4
Unequal Sample Sizes
. 480
12.3
Confidence Intervals for the Treatment Means: Contrasts
. 482
12.3.1
Multiple Comparisons of Treatment Means
. 485
12.4
Random Effects Model
. 487
12.5
Mathematical Derivations and Details
. 489
12.6
Chapter Summary
. 490
12.7
Problems
. 490
12.8
To Probe Further
. 496
13
Design and Analysis of Multi-Factor Experiments
497
13.1
Orientation
. 497
13.2
Randomized Complete Block Designs
. 498
13.2.1
Confidence Intervals and Multiple Comparison Procedures
. 507
13.2.2
Model Checking via Residual Plots
. 508
13.3
Two Factor Experiments with
η
> 1
Observations per Cell
. 508
13.3.1
Confidence Intervals and Multiple Comparisons
. 520
13.4
2fc Factorial Designs
. 522
13.5
Chapter Summary
. 540
13.6
Problems
. 540
13.7
To Probe Further
. 548
14
Statistical Quality Control
551
14.1
Orientation
. 551
14.2
χ
and
R
Control Charts
. 552
14.2.1
Detecting a Shift in the Process Mean
. 557
14.3
p
Charts and
с
Charts
. 559
14.4
Chapter Summary
. 562
14.5
Problems
. . . .*. 562
14.6
To Probe Further
. 565
A Tables
567
A.I Cumulative Binomial Distribution
. 568
A.
2
Cumulative
Poisson
Distribution
. 570
A.3 Standard Normal Probabilities
. 572
A.
4
Critical Values tu(a) of the
t
Distribution
. 574
A.5 Quantiles Qu(p)
=
χΙ(1 -ρ)
of the
χ2
Distribution
. 575
A.6 Critical Values of the FVl
,„2
(α)
Distribution
. 576
A.
7
Critical Values of the Studentized Range q(a; n^v)
. 580
A.8 Factors for Estimating
σ,
5,
or
ацмѕ
and
ац
from
R
. 584
A.9 Factors for Determining from
R
the Three-Sigma Control Limits for X and
R
Charts
.„ . . 585
A.
10
Factors for Determining from
σ
the Three-Sigma Control Limits for X, R,
and
s
or
σ
амѕ
Charts
. 586
Answers to Selected Odd-Numbered Problems
589
1
Data Analysis
591
2
Probability Theory
597
3
Discrete Random. Variables and Their Distribution Functions
601
4
Continuous Random Variables and Their Distribution Functions
609
5
Multivariate Probability Distributions
617
6
Sampling Distribution Theory
623
7
Point and Interval Estimation
625
8
Hypothesis Testing
631
9
Statistical Analysis of Categorical Data
637
10
Linear Regression and Correlation
641
11
Multiple Linear Regression
645
12
Single Factor Experiments: Analysis of Variance
647
13
Design and Analysis of Multi-Factor Experiments
653
14
Statistical Quality Control
659
Index
661 |
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| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
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| id | DE-604.BV023371291 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:12:40Z |
| indexdate | 2024-07-09T21:17:04Z |
| institution | BVB |
| isbn | 1584888121 9781584888123 |
| language | English |
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| physical | 667 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2009 |
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| publisher | CRC Press |
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| spelling | Rosenkrantz, Walter A. Verfasser aut Introduction to probability and statistics for science, engineering, and finance Walter A. Rosenkrantz Probability and statistics for science, engineering, and finance Boca Raton [u.a.] CRC Press 2009 667 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier "A Chapman & Hall book." Includes bibliographical references and index Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf 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=016554548&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosenkrantz, Walter A. Introduction to probability and statistics for science, engineering, and finance Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4056995-0 |
| title | Introduction to probability and statistics for science, engineering, and finance |
| title_alt | Probability and statistics for science, engineering, and finance |
| title_auth | Introduction to probability and statistics for science, engineering, and finance |
| title_exact_search | Introduction to probability and statistics for science, engineering, and finance |
| title_exact_search_txtP | Introduction to probability and statistics for science, engineering, and finance |
| title_full | Introduction to probability and statistics for science, engineering, and finance Walter A. Rosenkrantz |
| title_fullStr | Introduction to probability and statistics for science, engineering, and finance Walter A. Rosenkrantz |
| title_full_unstemmed | Introduction to probability and statistics for science, engineering, and finance Walter A. Rosenkrantz |
| title_short | Introduction to probability and statistics for science, engineering, and finance |
| title_sort | introduction to probability and statistics for science engineering and finance |
| topic | Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Probabilities Mathematical statistics Wahrscheinlichkeitsrechnung Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016554548&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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