Introduction to probability and statistics:
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| Previous Title: | Brief course in statistical theory |
|---|---|
| Main Authors: | , , |
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
MacMillan [u.a.]
1978
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 356 S. graph. Darst. |
| ISBN: | 0023709006 |
Staff View
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| 100 | 1 | |a Lindgren, Bernard W. |d 1924- |e Verfasser |0 (DE-588)172227216 |4 aut | |
| 245 | 1 | 0 | |a Introduction to probability and statistics |c B. W. Lindgren ; G. W. MacElrath ; D. A. Berry |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a New York [u.a.] |b MacMillan [u.a.] |c 1978 | |
| 300 | |a XII, 356 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Probabilités | |
| 650 | 4 | |a Statistique mathématique | |
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Record in the Search Index
| _version_ | 1804118009112952832 |
|---|---|
| adam_text | Contents
1
PROBABILITY MODELS
1.1 Mathematical models 2
1.2 Sample spaces and events 5
1.3 Probability 10
1.4 Discrete sample spaces 11
1.5 A priori models 13
1.6 Populations 15
2
COUNTING
2.1 A basic principle 19
2.2 Permutations 22
2.3 Combinations 24
* 2.4 Binomial and multinomial coefficients 27
vii
viii Contents
3
DISCRETE RANDOM VARIABLES
3.1 Distributions in the value space 33
3.2 Expected value 37
3.3 Expected value of a function 41
3.4 Expectation as a Center of Gravity 43
3.5 Variance 44
3.6 Covariance 46
4
INDEPENDENCE
4.1 Conditional probability 52
4.2 Independent events 57
4.3 Composite experiments 58
4.4 Independent random variables 61
5
BERNOULLI POPULATIONS
5.1 Sampling a Bernoulli population 67
5.2 The binomial distribution 68
5.3 Hypergeometric probabilities 71
* 5.4 Inverse sampling 75
6
CONTINUOUS RANDOM VARIABLES
6.1 Recording and presenting data 80
6.2 Density 83
6.3 The distribution function 91
6.4 Percentiles 95
6.5 Expected value 96
6.6 Several continuous variables 98
Contents ix
7
THE POISSON PROCESS
7.1 The Poisson random variable 104
7.2 The waiting time distribution 109
* 7.3 An alternative derivation 112
* 7.4 Randomness of events 114
* 7.5 Reliability 115
8
NORMAL DISTRIBUTIONS
8.1 The standard normal distribution 120
8.2 The normal family 122
8.3 The central limit theorem 124
8.4 Approximating binomial probabilities 127
* 8.5 Approximating Poisson probabilities 130
* 8.6 Errors 131
9
SAMPLES
9.1 Random sampling 137
9.2 Random numbers 138
9.3 Statistics 139
9.4 Linear transformations 145
9.5 Sampling distributions 146
9.6 Sampling distribution of the mean 147
10
ESTIMATION
10.1 Mean squared error 153
10.2 Estimating the mean—Large samples 154
10.3 Estimating a proportion 156
x Contents
~k 10.4 Estimating a standard deviation 158
10.5 Interval estimates for n 160
10.6 Interval estimates for p 163
* 10.7 Interval estimates for o 165
•k 10.8 Maximum likelihood estimation 167
11
TESTING HYPOTHESES
11.1 Hypothesis testing—General 173
11.2 Large sample tests for fi 179
11.3 Small sample tests for fi—Normal case 181
11.4 Tests and confidence intervals 183
11.5 A rank test for location 184
11.6 Power 186
• 11.7 Goodness of fit 193
11.8 Statistical and practical significance 196
12
COMPARING LOCATIONS
12.1 Tests based on means 202
12.2 Confidence interval for Ap 205
12.3 A two sample rank test 206
12.4 Paired data 210
12.5 More on significance 212
13
BAYESIAN INFERENCE
13.1 Nature as a random variable 219
13.2 From prior to posterior distribution 220
13.3 Making a decision 223
13.4 Testing a simple hypothesis against a simple alternative 225
13.5 Bayesian estimation 226
13.6 How large a sample? 230
Contents xi
14
SEQUENTIAL TESTING
14.1 An example 234
14.2 Likelihood 235
14.3 The sequential likelihood ratio test 238
14.4 Composite hypotheses 240
15
TESTS FOR CATEGORICAL POPULATIONS
15.1 The chi square goodness of fit test 246
15.2 Models with unknown parameters 248
15.3 Bernoulli populations 249
15.4 Independence 252
15.5 Testing for a relationship 255
16
CORRELATION AND REGRESSION
16.1 Prediction 262
16.2 The method of least squares 264
16.3 Inference for linear regression 268
17
ANALYSIS OF VARIANCE
17.1 A single factor 275
17.2 Two factors 283
17.3 On analysis and design 288
xii Contents
18
SOME INDUSTRIAL APPLICATIONS
18.1 Sampling inspection by attributes 293
18.2 Control charts 298
A
Appendix Ji JL
GENERATING FUNCTIONS
A.I The moment generating function 307
A.2 Factorial moment generating functions 309
A.3 Sums of independent variables 311
A.4 Probability generating functions 312
R
Appendix JLM
TABLES 315
ANSWERS 349
INDEX 355
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| indexdate | 2024-07-09T16:03:29Z |
| institution | BVB |
| isbn | 0023709006 |
| language | English |
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| spelling | Lindgren, Bernard W. 1924- Verfasser (DE-588)172227216 aut Introduction to probability and statistics B. W. Lindgren ; G. W. MacElrath ; D. A. Berry 4. ed. New York [u.a.] MacMillan [u.a.] 1978 XII, 356 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilités Statistique mathématique Mathematical statistics Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s MacElrath, Gayle William Verfasser (DE-588)1058150405 aut Berry, Donald A. 1940- Verfasser (DE-588)136565514 aut Frueher u.d.T. Brief course in statistical theory HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lindgren, Bernard W. 1924- MacElrath, Gayle William Berry, Donald A. 1940- Introduction to probability and statistics Probabilités Statistique mathématique Mathematical statistics Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4056995-0 (DE-588)4151278-9 |
| title | Introduction to probability and statistics |
| title_auth | Introduction to probability and statistics |
| title_exact_search | Introduction to probability and statistics |
| title_full | Introduction to probability and statistics B. W. Lindgren ; G. W. MacElrath ; D. A. Berry |
| title_fullStr | Introduction to probability and statistics B. W. Lindgren ; G. W. MacElrath ; D. A. Berry |
| title_full_unstemmed | Introduction to probability and statistics B. W. Lindgren ; G. W. MacElrath ; D. A. Berry |
| title_old | Brief course in statistical theory |
| title_short | Introduction to probability and statistics |
| title_sort | introduction to probability and statistics |
| topic | Probabilités Statistique mathématique Mathematical statistics Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Probabilités Statistique mathématique Mathematical statistics Probabilities Wahrscheinlichkeitsrechnung Statistik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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