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Hodges J. L., Lehmann E. L. — Basic Concepts Of Probability And Statistics
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Название: Basic Concepts Of Probability And Statistics
Авторы: Hodges J. L., Lehmann E. L.
Аннотация: Basic Concepts of Probability and Statistics provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background. It is the only book at this level to introduce readers to modern concepts of hypothesis testing and estimation, covering basic concepts of finite, discrete models of probability and elementary statistical methods. Although published in 1970, it maintains a modern outlook, especially in its emphasis on models and model building and also by its coverage of topics such as simple random and stratified survey sampling, experimental design, and nonparametric tests and its discussion of power.The book covers a wide range of applications in manufacturing, biology, and social science, including demographics, political science, and sociology. Each section offers extensive problem sets, with selected answers provided at the back of the book. Among the topics covered that readers may not expect in an elementary text are optimal design and a statement and proof of the fundamental (NeymanPearson) lemma for hypothesis testing.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Издание: 2-е издание
Год издания: 2005
Количество страниц: 462
Добавлена в каталог: 17.11.2013
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Предметный указатель
Events, intersection of two 29 31
Events, simple 12 18
Events, union of two 31 see
Examination see "Multiple-choice"
Exclusive events 30 33 35 102
Expectation 142 147 149
Expectation as center of gravity 148
Expectation as expectation of conditional expectation 223
Expectation as long-run average 142
Expectation of average 267
Expectation of binomial 170
Expectation of hypergeometric 175 180
Expectation of indicator 148
Expectation of matching 153
Expectation of measurement 266
Expectation of Poisson 202
Expectation of sample average 262
Expectation of uniform 205 207
Expectation of weighted average 253
Expectation of Wilcoxon paired-comparison statistic 359
Expectation of Wilcoxon two-sample statistic 342 343
Expectation, addition law of 151
Expectation, conditional 221
Expectation, minimizes expected squared error 165
Expectation, multiplication law of 154
Expected value 142 see
Expenses see "Medical"
Experiment see "Size"
Experiment with several parts 62 see
Experiment, deterministic 3
Experimental design see "Design"
Extrasensory perception 310 313
extreme values 290
Face card see "Heart"
Factor model 64 98
Factorial 59
Factorial design 296
Failure 77
Fair die 89
Fair price (for a game) 142
False acceptance 370 373
False negative (positive) 113
False rejection 311 373
Families see "Number" "Sequentially" "Sex" "Two-child"
Father-daughter marriage 127
Favorable cases 24
Federalist papers 129
Fertilizer 326
Field trials see "Agricultural"
Fisher — Irwin test 334 362
Fisher, R.A. 296 334 405
Floods 26
Forecasting see "Election"
frequency 5 13 17
Frequency of males 7 9 15 25 215
Frequency, conditional 69 89 91 97
Frequency, long-run 9 13 18 250
Frequency, stability property of 9 10
Frequency, unrelated 70 73
Galileo 309
gallery see "Shooting"
gambling 23 79 142
Gambling systems 144 147
Gambling, odds in personal probability 127
Gambling, systems 144 146 147
Gauss, K.F. 157
Gene 117
Gene, lethal 118 125
General addition law for expectation 152
General addition law for variance 227
Generalized binomial trials model 81 200 211
Generalized equivalence law of ordered sampling 55 59 277
Generator see "Random"
Genetic counseling 119
Genotype 117
Girls see "Boy" "Distribution"
Goodness of fit 321
Gosset, W.S. 405
Graded response 332 339
Graunt, J. 20 389
Gross error 291
Growth hormone see "Effect"
Guilt see "Probability"
Hamilton, A. 129
Hands see "Poker"
Heart face card 98
Heart treatment 333 339 391
histogram 138
Histogram of estimates 244 246 249
Histogram of standardized variable 182 184 186
Histogram, empirical 192
Homogeneity of subjects 328 352
Hormone see "Effect"
hypergeometric 192 see
Hypergeometric distribution 138 174 239
Hypergeometric distribution in Fisher — Irwin test 333
Hypergeometric distribution, binomial approximation to 176
Hypergeometric distribution, expectation of 175
Hypergeometric distribution, multiple 219 234 235
Hypergeometric distribution, normal approximation to 192 280
Hypergeometric distribution, tables of 176
Hypergeometric distribution, variance of 177 229
Hypergeometric model 41 138 239 245 250 256
Hypergeometric model as lottery model 225
Hypergeometric model, estimation of proportion in 245 250 256 258 285
Hypergeometric model, testing of proportion in 374 379 383 see "Election "Lot "Proportion" "Quality "Sampling"
Hypergeometric random variable 138 174
Hypergeometric random variable as sum of indicators 175 176 178
Hypergeometric random variable in Fisher — Irwin test 333
Hypergeometric random variable, expectation of 143 175 178
Hypergeometric random variable, variance of 177 229
Hypothesis testing 241 310 see
improvement see "Quality"
Inclusion of a specified item 49
Income and politics 100
Independent events 73 98 102
Independent random variables 139
Independent random variables and central limit theorem 187
Independent random variables and zero correlation 226
Independent random variables in joint distributions 221 223 225
Independent random variables, addition law of variance for 163
Independent random variables, multiplication law of expectation for 155
Indicator (random variable) 138 141 150
Indicator (random variable), covariance of 164
Indicator (random variable), expectation of 148
Indicator (random variable), extended 395 see
Indicator (random variable), variance of 159
Indicators 138 148 159
Indirect dependence 72 100 126
Inspection see "Lot-Sampling" "Sampling"
Insufficient reason, principle of 24
Insulin and diabetes 100
Intelligence 265
Interaction 297 299
Intersection 29 31 see
Interval estimation 240
Inverse ranks 348
Irwin, J.O. 334
Items see "Choosing" "Defective" "Inclusion"
Items of several types 219
Items of three types 219
Joint distribution 218
Joint distribution, marginal 222 234
Judged response 362
Laboratories see "Two"
Laplace's measure of dispersion 158
Laplace, P.S. 158
Law of Large Numbers 210
Law of large numbers, uniform 211
Laws of averages 80
Laws of complementation 34
Laws of covariance 163 225 see "Bayes' "De "Equivalence "Law "Multiplication
Laws of expectation 151 152 154 155
Laws of variance 161 164 227 230
Lethal gene 118 125
level of significance 311 317 370
Life table 19 20 88 92
Life testing 401
Light see "Velocity"
List of simple results 12 18 24
Loaded dice 13 64 90 233 see "Two"
Loaded die 90 231 233 393 398
Long-run frequency 9 13 18 250
Long-run stability 4 208 210
Lot sampling 78 219 234 239 374 379 see "Sampling" "Defectives"
Lot-sampling inspection 374
Lotions see "Sun-Tan"
Lottery 144 152 158 see
Lottery model see "Variance"
Lottery model (for sampling by variables) 144 152 158 164 261
Lottery model (for sampling by variables) as basis for Wilcoxon two-sample test 343 364 384 see "Hypergeometric
Lottery model (for sampling by variables) as model for outliers 290
Lottery model (for sampling by variables), approximation by repeated measurements model 236
Lottery model (for sampling by variables), comparison of two 273
Lottery model (for sampling by variables), covariance in 228
Lottery model (for sampling by variables), estimation of variance in 283 285
Lottery model (for sampling by variables), hypergeometric model as special case of 228
Lottery model (for sampling by variables), sample size in 262
Lottery model (for sampling by variables), stratification of 300
Lottery model (for sampling by variables), variance of sample mean in 227 262
Lottery model (for sampling by variables), weighted means in 289
Lunch counter 48
Lung cancer see "Smoking"
Madison, J. 129
Main effect 297
Male births 7 191
Mann — Whitney test 347 see
Marginal distribution 220 222
Marginal distribution of multinomial distribution 234
Marksmen 171
Mass production see "Defective"
Matched pairs 352 358 see
Matching 153 316
Matching distribution 205 208
Matching distribution in testing for randomness 310 313 316 385 see
Matching distribution, expectation of 153
Matching distribution, Poisson approximation for 207
Matching distribution, table of 206 208
Matching distribution, variance of 207 230
Matchings see "Number"
Mathematical model 11
Mean rank method 363 365
Mean square deviation 159 see
Measured quantities see "Comparison"
Measurement 4 265
Measurement, error 265
Measurement, model 266 401 see
Measurements see "Repeated" "Several"
Measuring a distance 4
Median 22 149 291
Medical expenses 260
Mendel, G. 117
Mendelian theory 118 391
Method of indicators 153 170 175 178 216 361 see
Model see "Binomial" "Hypergeometric" "Variance"
Model for ordered sampling 53 92 110
Model for repeated measurements 267 281 288 401 see "Double "Hypergeometric" "Lottery" "Probability
Model for sampling 42 261 269
Model for several measurements 266 278
Model for two-stage experiments 108 112
Model, factor 64
Model, mathematical 11
Model, measurement 266
Model, multinomial 231 321
Model, uniform 23
Moment of inertia 157
Multinomial distribution 232
Multinomial distribution in chi-square test 321
Multinomial distribution, marginal and conditional 234 235
Multinomial distribution, probability ratio test for 398
Multinomial, (trials) model 231 321 398
Multinomial, random variables 232
Multinomial, trials 81 84 231
Multiple hypergeometric distribution 219 234 235
Multiple-choice examination 168
Multiple-choice quiz 64
Multiplication law for probabilities 97 156
Multiplication law of expectation 154 157 see "Independent "Product
Neyman — Pearson fundamental lemma 396 399
Neyman, J. v 304 308 396 399
Nonparametric tests vii 331 see "Sign" "Wilcoxon
Normal approximation 190
Normal approximation in estimation problems 251
Normal approximation in hypothesis testing 318 378 380 395
Normal approximation, failure of 193
Normal approximation, to -test 402
Normal approximation, to binomial 191 210
Normal approximation, to Fisher — Irwin test 335
Normal approximation, to hypergeometric 192 380
Normal approximation, to Poisson 202
Normal approximation, to power 372 395 403
Normal approximation, to Wilcoxon 342 359 364 366
Normal curve 185 192
Normal curve, figure of 185
Normal curve, table for 416
Normal curve, use of table of 187
Normally distributed observations 405
Null distribution see "Computation"
Null hypothesis 310 316
Number of arrangements 58
Number of boys in a two-child family 132 133
Number of combinations 47 see
Number of matchings 132 133 205
Number of matchings as sum of indicators 154 230
Number of matchings in testing for randomness 310 313 316 385 see
Number of matchings, expectation of 153
Number of matchings, variance of 207 230
Number of ordered samples 53 55 58
Number of ordered samples, table of 53
Number of permutations 53 see
Number of samples (or combinations) 42 47
Number of samples (or combinations), formulas for 51 54 59 60
Number of samples (or combinations), generalized 233
Number of samples (or combinations), tables of 42 48 412
Odds ratio 151 247
One-sample problem 360
One-sided test 390
Optimum, allocation 293 298 303 307
Optimum, test 396
Optimum, weights of weighted average 288 307
Ordered sample 52 see
Ordered sampling 52 58 92 110
Ordered sampling, equivalence law of 55 59 see
Outliers 290
Paired comparisons 330 352 357
PARAMETER 240 245 389
Part of an experiment 62
Pascal's triangle 48
Pearson, E.S. 396 399
Pearson, K. 321
Pennies see "Tossing" "Two"
Penny and dime 70
Perception see "Extrasensory"
permutations 53 see
Personal probability 127
Petersburg game 146
Physics by TV 327
pictures see "Baby"
Placebo effect 337
Poetry quiz 385
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