A guide to probability theory and application
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| Format: | Buch |
| Sprache: | English |
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New York
Holt, Rinehart and Winston
1973
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| Schriftenreihe: | International series in decision processes.
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| 245 | 1 | 0 | |a A guide to probability theory and application |c Cyrus Derman ; Leon J. Gleser ; Ingram Olkin |
| 264 | 1 | |a New York |b Holt, Rinehart and Winston |c 1973 | |
| 300 | |a XVI,750 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a International series in decision processes. | |
| 650 | 4 | |a Probabilités | |
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Datensatz im Suchindex
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| adam_text | CONTENTS
Preface ix
PART I FUNDAMENTAL CONCEPTS
1 Introduction 3
1 History, 3
2 Models, 5
3 The Empirical Basis of Probability Theory, 8
4 Notes and References, 15
2 The Elements of Probability Theory 25
1 Preliminaries, 25
2 Formal Structure: Outcomes and Event Sets, 25
Equality of Event Sets, 28
Inclusion of Event Sets, 29
The Union of Event Sets, 30
The Intersection of Event Sets, 31
The Complement of an Event Set, 31
Mutually Exclusive Event Sets, 34
Some Useful Rules, 35
The Correspondence between the Probability Model and Random Experi¬
ments, 38
3 Formal Structure: Probabilities, 40
4 The Probability Calculus, 42
Law of Inclusion, 42
Law of Complementation, 43
Law of Addition, 45
xi
xii CONTENTS
5 Fitting a Probability Model. 51
6 Notes and References, 54
3 Further Concepts of Probability Theory 65
1 Finite Probability Models, 66
2 Simple Random Sampling, 69
3 Composite Random Experiments, 72
A Comment on Notation, 74
4 Conditional Probability, 79
The Probability Calculus for Conditional Probabilities, 83
Law of Multiplication, 86
Law of Multiplication for Nested Events, 89
Partitions. 93
Bayes Rule, 95
5 Independence, 97
6 Appendix: Combinatorial Analysis, 100
Orderings and Permutations, 100
Orderings with Similar Elements, 101
Ordering of r Items from n, 104
Counting of Sets of Items, 105
7 Notes and References, 108
4 Random Variables 125
1 Random Variables, 125
2 Discrete and Continuous Random Variables, 130
3 Cumulative Distribution Functions, 133
Estimating the Cumulative Distribution Function from Data, 143
Mixed Discrete and Continuous Variables and their Cumulative Distribution
Functions, 144
4 Probability Mass Functions of Discrete Random Variables, 146
Estimating a Probability Mass Function: Bar Graphs, 149
5 Density Functions, 150
* Rectangular Probability Approximations, 153
Empirical Distributions: Histograms, 160
5 Descriptive Properties of Distributions 175
1 Introduction, 175
2 Measures of Location for a Distribution: The Expected Value, 177
The Expected Value of a Discrete Random Variable, 177
*The Expected Value of a Discrete Random Variable Having an Infinite
N umber of Possible Values, 185
The Expected Value of a Continuous Random Variable, 186
*Useof the Rectangular Method of Approximation, 188
The Expected Value as a Measure of Location, 191
Notation and Terminology, 193
3 Other Measures of Location for a Distribution: Median, Quantile,
Mode, 193
CONTENTS xiii
Medians, 193
Quantiles, 197
Modes, 203
Choice of a Measure of Location, 205
4 Measures of Dispersion for a Distribution: The Variance, 210
5 Higher Moments, 217
6 Inequalities for Probabilities, 223
Proof of the Markov Inequality, 224
Use of the Markov Inequality, 225
Supplementary Reading, 231
7 Appendix, 233
PART II PROBABILITY MODELS
6 Special Distributions: Discrete Case 247
1 Bernoulli and Binomial Distributions, 247
Bernoulli Distribution, 248
Binomial Distribution, 249
Tables, 255
2 Hypergeometric Distribution, 256
Derivation of the Hypergeometric Distribution, 258
Approximation of the Hypergeometric Distribution by the Binomial Distri¬
bution, 262
Uses of the Hypergeometric Distribution, 262
Description of Tables, 264
3 Poisson Distribution, 265
A Method for Fitting the Poisson Distribution, 266
Applications of the Poisson Distribution, 269
The Poisson Distribution as an Approximation of the Binomial Distribution,
272
Tables of the Poisson Distribution, 273
4 Geometric Distribution, 274
A Method for Fitting the Geometric Distribution, 277
Description of Tables of the Geometric Distribution, 279
Notes and References. 279
5 Negative Binomial Distribution, 280
*Generalization of the Negative Binomial Distribution, 284
* A Method for Fitting the Negative Binomial Distribution, 287
Applications of the Negative Binomial Distribution. 290
Description of Tables of the Negative Binomial Distribution, 292
6 Discrete Uniform Distribution, 293
Lotteries, 294
Generalized Discrete Uniform Distribution. 295
7 *Other Discrete Distributions, 296
The Zeta Distribution, 296
The Truncated Poisson Distribution. 299
References to Other Discrete Distributions, 304
8 Summary of Discrete Distribution, 304
xiv CONTENTS
7 The Normal Distribution 324
1 Introduction, 324
History, 326
2 Probability Calculations for the Normal Distributions, 332
Tail Probabilities, 336
Probabilities of Intervals of Numbers, 339
3 Fitting a Normal Distribution, 341
4 The Central Limit Theorem, 345
* A Justification of the Normal Distribution by the Central Limit Theorem, 349
8 Special Distributions: Continuous Case 358
1 The Exponential Distribution, 359
Fitting the Exponential Distribution to Data, 361
Probability Calculations, 364
The Survival Function, 365
An Interesting Property of the Exponential Distribution, 367
Notes and References, 368
2 The Gamma Distribution, 369
The Standard Gamma Density Function, 370
Fitting the Gamma Distribution to Data, 372
Probability Calculations, 374
3 *The Weibull Distribution, 378
A Theoretical Explanation, 385
Fitting the Weibull Distribution to Data, 385
The Survival Function, 389
4 The Uniform Distribution, 391
Probability Calculations, 393
Applications, 396
5 *The Beta Distribution, 398
Fitting the Beta Distribution to Data, 404
Probability Calculations, 405
Notes and References, 409
6 * Other Continuous Distributions, 410
The Lognormal Distribution, 410
The Cauchy Distribution, 414
Notes and References, 418
9 Multivariate Distributions 432
1 Introduction, 432
2 Discrete Bivariate Distributions, 433
Marginal Distributions, 439
Example of the Construction of a Bivariate Probability Model, 443
Conditional Distributions, 446
The Regression Function, 450
3 Descriptive Properties of Bivariate Distribution, 453
Rescaling Techniques, 460
The Correlation Coefficient, 464
CONTENTS xv
Correlation and Statistical Independence, 469
Correlation and Statistical Dependence, 472
4 Continuous Bivariate Distributions, 475
Marginal Probability Density Functions, 479
Conditional Probability Density Functions, 482
Statistical Independence, 483
Descriptive Properties of Bivariate Continuous Distributions, 484
5 The Bivariate Normal Distribution, 486
The Probability Contours of a Bivariate Normal Distribution, 490
The Standard Bivariate Normal Distribution, 493
6 *Some Multivariate Generalizations: Trivariate Discrete Distributions,
501
Conditional Distributions and Partial Correlation Coefficients, 506
Statistical Independence, 508
The Multinomial Distribution, 509
10 Weighted Sum of Random Variables 519
1 Standardization of Random Variables, 519
2 Weighted Sums of Random Variables, 523
Some Special Cases, 526
Expected Values and Variances, 527
3 The Law of Large Numbers, 530
4 Further Comments on the Central Limit Theorem, 533
The Continuity Correction, 539
5 *Appendix: Moment Generating Functions, 541
11 Markov Chains 550
1 Introduction, 550
2 Markov Chains, 552
3 Applications, 559
An Example from Psychology, 559
Social Processes, 563
Genetics, 566
4 Calculation of Step Transition Probabilities, 571
2 Step Transition Probabilities, 572
3 Step Transition Probabilities, 578
General it Step Transition Probabilities, 582
An Alternative Method for Calculating £ Step Transition Probabilities, 587
5 Absolute or Unconditional Probabilities, 588
12 * Markov Chains II: First Passage Times, Recurrent States,
and Long Run Probabilities 597
1 First Passage Times, 597
Calculation of the Probability Distribution of the First Passage Time K,,, 600
Infinite First Passage Times, 611
2 Recurrent and Transient States, 615
xvi CONTENTS
3 Expected First Passage Times, 620
Alternate Computation for Expected First Passage Times, 623
4 Probabilistic Equilibrium of a Markov Chain, 630
5 Classes of States, 634
Classes of Communicating States, 636
6 Aperiodic, Irreducible Markov Chains, 640
Periodic States and Periodic Chains, 642
Aperiodic States, 644
Steady State Equations, 648
7 Absorbing Markov Chains, 651
8 Notes and References, 657
Bibliography 663
Tables 671
Answers 717
Name Index 743
Subject Index 745
|
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| language | English |
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| spelling | Derman, Cyrus 1925-2011 Verfasser (DE-588)170709280 aut A guide to probability theory and application Cyrus Derman ; Leon J. Gleser ; Ingram Olkin New York Holt, Rinehart and Winston 1973 XVI,750 S. txt rdacontent n rdamedia nc rdacarrier International series in decision processes. Probabilités Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Gleser, Leon Jay Verfasser aut Olkin, Ingram 1924-2016 Verfasser (DE-588)118889036 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001962175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Derman, Cyrus 1925-2011 Gleser, Leon Jay Olkin, Ingram 1924-2016 A guide to probability theory and application Probabilités Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4064324-4 |
| title | A guide to probability theory and application |
| title_auth | A guide to probability theory and application |
| title_exact_search | A guide to probability theory and application |
| title_full | A guide to probability theory and application Cyrus Derman ; Leon J. Gleser ; Ingram Olkin |
| title_fullStr | A guide to probability theory and application Cyrus Derman ; Leon J. Gleser ; Ingram Olkin |
| title_full_unstemmed | A guide to probability theory and application Cyrus Derman ; Leon J. Gleser ; Ingram Olkin |
| title_short | A guide to probability theory and application |
| title_sort | a guide to probability theory and application |
| topic | Probabilités Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilités Probabilities Wahrscheinlichkeitsrechnung |
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