Applications of probability and random variables:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
McGraw-Hill
1974
|
| Edition: | 2. ed. |
| Series: | McGraw-Hill series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 448 S. graph. Darst. |
| ISBN: | 0070676518 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applications of probability and random variables |c George P. Wadsworth ; Joseph G. Bryan |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b McGraw-Hill |c 1974 | |
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Record in the Search Index
| _version_ | 1804121688159289344 |
|---|---|
| adam_text | CONTENTS
Preface to the Second Edition xi
Preface to the First Edition xiii
1 Probability Concepts 1
1 1 Introduction 1
1 2 Concept of Probability 2
1 3 Relative Frequency 5
1 4 Laws of Probability 8
1 5 Fundamental Theorems 9
1 6 General Comments 14
1 7 Illustrations of General Principles 15
1 8 Bayes Theorem 23
1 9 Geometrical Probability 27
Appendix to Chapter 1 32
1 10 Permutations and Combinations 32
Problems 35
Vi CONTENTS
2 Discrete Random Variables 39
2 1 Introduction 39
2 2 Distributions 40
2 3 Distribution Functions 41
2 4 Probability Functions 43
2 5 Random Sampling 45
2 6 Specific Discrete Distributions 46
2 7 The Binomial Distribution 46
2 8 The Multinomial Distribution 53
2 9 The Hypergeometric Distribution 55
2 10 The Geometric and Pascal Distribution 60
2 11 The Poisson Distribution 61
Problems 71
3 Probability and Difference Equations 74
3 1 Difference Equations 74
3 2 Probability Generating Functions 79
3 3 Simultaneous Difference Equations 82
3 4 Applications 87
3 5 Random Walks 87
3 6 Generalized Binomial Distribution 89
3 7 Sequence of Successes 91
Problems 93
4 Continuous Random Variables 96
4 1 Distribution Functions 96
4 2 Use of Distribution Functions in Defining Distributions 97
4 3 Computation of Probabilities 101
4 4 Density Functions 101
4 5 Properties of Density Functions 103
4 6 Examples of Density Functions 103
4 7 Use of Density Functions in Defining Distributions 105
4 8 Exceptional Situations 105
4 9 The Gamma Distribution 108
4 10 The Beta Distribution 123
4 11 The Normal Distribution 127
4 12 Confidence Limits (Interval Estimation) 136
Appendix to Chapter 4 139
CONTENTS vii
4 13 Gamma Functions 139
4 14 Beta Functions 142
Problems 145
5 Joint Distributions 149
5 / Fundamental Concepts 149
5 2 Multivariate distribution Functions and Density Functions 154
5 5 Admissible Regions 156
5 4 Continuous Bivariate Distributions 158
J J Illustrations of the Use of General Principles 165
5 6 Point Estimation of a Parameter 178
5 7 Bayesian Approach to Estimation 180
5 8 Search Theory and Distribution of Effort 187
Problems 192
6 Derived Distributions 198
6 1 Introduction 198
6 2 Monotonic Functions 199
6 3 The Density Function of a Monotonically Increasing Function 199
6 4 The Density Function of a Monotonically Decreasing Function 203
6 5 The Probability Transformation 205
6 6 Density Functions of the Square and the Absolute Value 206
6 7 The Distribution of a Function of Two or More Independent
Variates 207
6 8 Some Derived Distributions Used in Statistics 216
6 9 The Chi square Distribution 217
6 10 The t Distribution 218
6 11 The F Distribution 219
6 12 The Distribution of a Function of Nonindependent Variates 220
6 13 Joint Distribution of Multivariate Functions 224
6 14 Significance Tests 236
6 15 The Hypergeometric Test for the Difference between Two
Percentages 246
6 16 Collective Significance 250
Problems 254
7 Mathematical Expectation 260
7 1 Definition 260
7 2 Averages 262
viii CONTENTS
7 3 Some Additional Properties of the Mean 267
7 4 Variance 268
7 5 Unbiased Estimation of Variance 273
7 6 Probability of Extreme Values 276
7 7 Multivariate Functions 278
7 8 Covariance and Correlation 281
7 9 The Variance of a Linear Function 282
7 70 Applications of Expected value Theory 283
Problems 302
8 Generating Functions 309
8 1 Moments 309
8 2 Characterization of a Distribution Function 310
8 3 Characteristic Functions 313
8 4 Moment generating Functions 316
8 5 Multivariate Moment generating Functions 326
8 6 Asymptotic Distributions 329
Problems 336
9 Markov Processes and Waiting Lines 339
9 1 Definition 339
9 2 Mathematical Properties 340
9 3 Difference Equations 342
9 4 Ergodic Process 346
9 5 Markov Processes and Rewards 353
9 6 Strategies and Markov Processes 357
9 7 Continuous Markov Processes 360
9 8 Illustrations of Continuous Markov Processes 366
Appendix to Chapter 9 374
9 9 Convergence of the Maximization Program 374
Problems 375
10 Some Statistical Uses of Probability 379
10 1 Introduction 379
10 2 The Normal Tests 380
10 3 The Normal Test for the Difference between Two Percentages 380
10 4 The Normal Test for Association or Independence 385
CONTENTS IX
10 5 The Chi square Tests 387
10 6 The Chi square Test for Goodness of Fit 388
10 7 The Chi square Test for Homogeneity 392
10 8 The Chi square Test for Association or Independence 395
10 9 The Distributions of x and s2 in a Normal Population 400
10 10 The t Tests 403
10 11 The t Test for a Single Mean 404
10 12 The t Test for the Means of Paired Observations 406
10 13 The t Test for the Difference of the Means of Two Independent
Samples 408
10 14 Respective Confidence Limits for i and a2 412
10 15 The F Tests 415
10 16 Tests for Equality of Variances 416
70 /7 The F Test for Equality of More Than Two Means 421
Problems 426
Index 443
|
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| dewey-raw | 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV007423824 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:01:57Z |
| institution | BVB |
| isbn | 0070676518 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004808015 |
| oclc_num | 618491 |
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| owner | DE-355 DE-BY-UBR DE-N32 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-N32 DE-19 DE-BY-UBM |
| physical | XV, 448 S. graph. Darst. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill series in probability and statistics |
| spelling | Wadsworth, George P. Verfasser aut Applications of probability and random variables George P. Wadsworth ; Joseph G. Bryan 2. ed. New York u.a. McGraw-Hill 1974 XV, 448 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in probability and statistics Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Operations Research (DE-588)4043586-6 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Bryan, Joseph G. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004808015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wadsworth, George P. Bryan, Joseph G. Applications of probability and random variables Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4057630-9 (DE-588)4043586-6 |
| title | Applications of probability and random variables |
| title_auth | Applications of probability and random variables |
| title_exact_search | Applications of probability and random variables |
| title_full | Applications of probability and random variables George P. Wadsworth ; Joseph G. Bryan |
| title_fullStr | Applications of probability and random variables George P. Wadsworth ; Joseph G. Bryan |
| title_full_unstemmed | Applications of probability and random variables George P. Wadsworth ; Joseph G. Bryan |
| title_short | Applications of probability and random variables |
| title_sort | applications of probability and random variables |
| topic | Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Probabilities Wahrscheinlichkeitsrechnung Stochastischer Prozess Operations Research |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004808015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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