Introductory probability and statistical applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1970
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| Edition: | 2. ed. |
| Series: | Addison-Wesley world student series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 367 S. graph. Darst. |
| ISBN: | 0201047101 |
Staff View
MARC
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| 100 | 1 | |a Meyer, Paul L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory probability and statistical applications |c Paul L. Meyer |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1970 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1 Introduction to Probability
1.1 Mathematical models 1
1.2 Introduction to sets 3
1.3 Examples of nondeterministic experiments 6
1.4 The sample space 8
1.5 Events 10
1.6 Relative frequency 12
1.7 Basic notions of probability 13
1.8 Several remarks 17
Chapter 2 Finite Sample Spaces
2.1 Finite sample spaces 21
2.2 Equally likely outcomes 22
2.3 Methods of enumeration 24
Chapter 3 Conditional Probability and Independence
3.1 Conditional probability 33
3.2 Bayes theorem 39
3.3 Independent events 41
3.4 Schematic considerations; conditional probability and independence . 46
Chapter 4 One Dimensional Random Variables
4.1 General notion of a random variable 54
4.2 Discrete random variables 59
4.3 The binomial distribution 62
4.4 Continuous random variables 66
4.5 Cumulative distribution function 70
4.6 Mixed distributions 73
4.7 Uniformly distributed random variables 74
4.8 A remark 76
xi
xii Contents
Chapter 5 Functions of Random Variables
5.1 An example 81
5.2 Equivalent events 81
5.3 Discrete random variables 84
5.4 Continuous random variables 85
Chapter 6 Two and Higher Dimensional Random Variables
6.1 Two dimensional random variables 93
6.2 Marginal and conditional probability distributions 99
6.3 Independent random variables 103
6.4 Functions of a random variable 106
6.5 Distribution of product and quotient of independent random variables 109
6.6 n dimensional random variables 112
Chapter 7 Further Characterization of Random Variables
7.1 The expected value of a random variable 117
7.2 Expectation of a function of a random variable 123
7.3 Two dimensional random variables 127
7.4 Properties of expected value 128
7.5 The variance of a random variable 134
7.6 Properties of the variance of a random variable 136
7.7 Approximate expressions for expectation and variance 139
7.8 Chebyshev s inequality 141
7.9 The correlation coefficient 144
7.10 Conditional expectation 148
7.11 Regression of the mean 150
Chapter 8 The Poisson and Other Discrete Random Variables
8.1 The Poisson distribution 159
8.2 The Poisson distribution as an approximation to the
binomial distribution 160
8.3 The Poisson process 165
8.4 The geometric distribution 170
8.5 The Pascal distribution 173
8.6 Relationship between the binomial and Pascal distributions . . . 174
8.7 The hypergeometric distribution 175
8.8 The multinomial distribution 176
Chapter 9 Some Important Continuous Random Variables
9.1 Introduction 182
9.2 The normal distribution 182
9.3 Properties of the normal distribution 183
9.4 Tabulation of the normal distribution 186
9.5 The exponential distribution 190
9.6 Properties of the exponential distribution 190
Contents xiii
9.7 The Gamma distribution 193
9.8 Properties of the Gamma distribution 194
9.9 The chi square distribution 196
9.10 Comparisons among various distributions 198
9.11 The bivariate normal distribution 199
9.12 Truncated distributions 200
Chapter 10 The Moment Generating Function
10.1 Introduction 209
10.2 The moment generating function 210
10.3 Examples of moment generating functions 211
10.4 Properties of the moment generating function 213
10.5 Reproductive properties 217
10.6 Sequences of random variables 221
10.7 Final remark 222
Chapter 11 Applications to Reliability Theory
11.1 Basic concepts 225
11.2 The normal failure law 228
11.3 The exponential failure law 229
11.4 The exponential failure law and the Poisson distribution .... 232
11.5 The Weibull failure law 234
11.6 Reliability of systems 235
Chapter 12 Sums of Random Variables
12.1 Introduction 244
12.2 The law of large numbers 244
12.3 Normal approximation to the Binomial distribution 247
12.4 The central limit theorem 250
12.5 Other distributions approximated by the normal distribution:
Poisson, Pascal, and Gamma 255
12.6 The distribution of the sum of a finite number of random variables . 256
Chapter 13 Samples and Sampling Distributions
13.1 Introduction 265
13.2 Random samples 266
13.3 Statistics 268
13.4 Some important statistics 269
13.5 The integral transform 275
Chapter 14 Estimation of Parameters
14.1 Introduction 282
14.2 Criteria for estimates 283
14.3 Some examples 286
14.4 Maximum likelihood estimates 290
xiv Contents
14.5 The method of least squares 299
14.6 The correlation coefficient 302
14.7 Confidence intervals 303
14.8 Student s ^ distribution 305
14.9 More on confidence intervals 307
Chapter 15 Testing hypotheses
15.1 Introduction 316
15.2 General formulation: normal distribution with known variance . . 321
15.3 Additional examples 325
15.4 Goodness of fit tests 328
References 338
Appendix 341
Answers to Selected Problems 357
Index 363
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV004152806 |
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| indexdate | 2024-07-09T16:09:08Z |
| institution | BVB |
| isbn | 0201047101 |
| language | English |
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| physical | XIV, 367 S. graph. Darst. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
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| publisher | Addison-Wesley |
| record_format | marc |
| series2 | Addison-Wesley world student series |
| spelling | Meyer, Paul L. Verfasser aut Introductory probability and statistical applications Paul L. Meyer 2. ed. Reading, Mass. [u.a.] Addison-Wesley 1970 XIV, 367 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley world student series Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Wahrscheinlichkeit (DE-588)4137007-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002589979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meyer, Paul L. Introductory probability and statistical applications Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4137007-7 (DE-588)4064324-4 (DE-588)4151278-9 |
| title | Introductory probability and statistical applications |
| title_auth | Introductory probability and statistical applications |
| title_exact_search | Introductory probability and statistical applications |
| title_full | Introductory probability and statistical applications Paul L. Meyer |
| title_fullStr | Introductory probability and statistical applications Paul L. Meyer |
| title_full_unstemmed | Introductory probability and statistical applications Paul L. Meyer |
| title_short | Introductory probability and statistical applications |
| title_sort | introductory probability and statistical applications |
| topic | Mathematical statistics Probabilities Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Mathematical statistics Probabilities Statistik Wahrscheinlichkeit Wahrscheinlichkeitsrechnung Einführung |
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