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Jeffreys H. — Theory of probability
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Название: Theory of probabilityАвтор: Jeffreys H. Аннотация: This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-nd editionГод издания: 1948Количество страниц: 416Добавлена в каталог: 08.12.2013Операции: Положить на полку |
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158 170 85 87 363 97 281 48 'Student' 94 122 205 219 271 350 364 A priori 8 29 Abbreviations x, dx 120 Accidents, factory 69 295 Accuracy, useful degree of 125 397 Adams, J.C. 389 Addition rule 19 30 33 Agreement, too close 281 Agricultural experiments 127 214 361 Aitken, John 60 Alternative hypothesis 220 Amoeba 6 Ancillary statistics 182 Applicability 8 9 11 Approximations 50 140 168 170 251 Argon 260 Arithmetic mean 84 92 107 189 Assent, universal 14 46 Atmospheric tide 307 Average residual 188 Barnes, E.W. 395 Bartlett, M.S. 41 53 147 Bateman, H. 59 Bayes, T. 29 30 34 42 102 107 109 374 Behaviourism 45 379 Belief see "Confidence" Benefit, expectation of 30 Bernoulli, Daniel 32 Bernoulli, James 52 Bias 143 177 231 Binomial law 50 56 Binomial, negative 68 77 Black, A.N. 174 Boltzmann 28 369 Bond, W.N. 288 Boys, C.V. 280 Broad, C.D. 5 26 111 112 115 372 Brown, E.W. 362 Brunt, D. 211 269 Bullard, E.C. 84 129 137 Bullen, K.E. 175 Burnside, W. 345 Campbell, N.R. 6 14 41 Cantelli, F.P. 55 Carnap, R. 20 Carroll, Lewis 45 220 305 407 Cauchy rule 78 81 170 189 244 Causality 12 108 Caution 273 287 381 Central limit theorem 79 Certainty on the data 17 Certainty, approach to 38 336 Chance 41 50 229 Chance, continuous distribution 301 Chance, games of 32 47 Chapman, S. 307 Characteristic function 73 Chauvenet 188 291 357 checking 139 Chesterton, G.K. 395 Combination of estimates 175 Combination of tests 305 Common sense 1 Comparison of chances 235 Comrie, L.J. 62 Confidence, reasonable degree of 15 Conjunction 18 Consistency 8 19 35 36 159 166 170 251 405 Continental drift 48 Contingency 211 232 Contingency, diagonal elements 332 Continuity 21 24 Continuous variation 227 Conventions 20 30 Correlation 71 152 263 Correlation, correction of 202 Correlation, internal 271 287 289 400 Correlation, intraclass 72 198 268 276 314 correlation, partial 328 Correlation, rank 204 268 Correlation, serial 170 227 328 Cournot, A. 374 Cramer, H. 80 343 Critical realism and idealism 46 Curvature of universe 304 Damoiseau 389 Data, need to state 15 27 350 377 de Moivre, A. 52 342 Deduction 1 3 17 Deduction as approximation 336 definitions 379 Degrees of freedom 89 128 Delauney 389 Density, probability 24 Design of experiments 97 214 361 Determinism 11 Deviation, standard 92 128 Diananda, P.H. 60 169 Dice 50 231 306 314 Digamma function 187 Dingle, H. 14 384 Dip, magnetic 84 Dirichlet integrals 87 116 Disjunction 18 Disjunction, separation of 41 Dodgson, C.L. see "Carroll Lewis" Dust counter 60 241 Earthquakes, aftershocks 325 334 Earthquakes, determination of epicentres 136 Earthquakes, identity of epicentres 322 Earthquakes, law of error 190 Earthquakes, periodicity 324 Earthquakes, travel times, P 175 202 273 299 Earthquakes, travel times, S and SKS 265 Economy of thought 4 Economy of thought of postulates 9 37 46 102 345 384 Edgeworth, F.Y. 108 Efficiency 145 179 Einstein, A. 362 386 Ellis, R.L. 345 374 Emmett, W.G. 365 Ensemble 11 341 Entailment 17 48 Epistemology 1 12 13 Equations of condition 133 Equations of condition, normal 133 Ergodic theory 371 Errors 12 13 see Errors, accidental 270 Errors, composition of 74 79 Errors, independence of 286 see internal" Errors, normal law 60 287 Errors, probable 62 124 Errors, standard 62 Errors, systematic 270 273 Errors, unknown law of 187 Estimation 99 Estimation, relation to significance 359 Euclid 8 40 exclusive 18 Exhaustive 18 Expectation of benefit 31 43 Expectation, mathematical 31 43 177 364 Expectation, moral 31 Explanation 303 390 Factorial function 51 239 Factory accidents 69 295 Fiducial argument 352 Fieller, E.C. 55 Fisher, R.A. 11 29 63 88 92 96 124 127 152 169 179 181 184 189 197 209 214 229 238 282 306 341 352 356 364 Franks, W.S. 211 Frechet, M. 371 Freedom, degrees of 89 128 Freeman, R.A. 100 392 Frequency definitions 11 34 342 372 Freud, S. 239 Functions, new 295 Functions, old 299 Gases, kinetic theory 28 369 Gauss, C.F. 14 62 84 103 133 190 Geiger, H. 59 Gender 239 Generalization (empirical propositions) 1 3 Generalization (logical propositions) 7 26 George, W.H. 12 Gibbs, Willard 11 341 369 Glaisher 390 Goedel, K. 35 56 Gosset, W.L. see "'Student'" Grades 206 210 Gravitation, constant of 280 Gravitation, law of 362 Gravity 129 137 198 Greenwood, M. 69 GROUPING 136 184 193 326 H (definition) 48 Haldane, J.B.S. 107 120 162 Heisenberg, H. 14 Heyl, P.R. 280 hilbert 10 Hill, G.W. 362 Horse, kicks by 59 71 295 Hulme, H.R. 288 Idealism 49 393 Ignorance 34 101 220 222 353 Implication 17 48 Impossibility 17 Induction 1 8 Infinite population 11 341 345 Infinite regress 112 116 375 407 Inoculation 239 312 Insufficient reason 34 Integer, unknown 213 Internal correlation 271 287 289 400 Intuition 15 Invariance 104 158 170 248 Inverse probability 29 35 372 Irrelevance 28 41 42 160 163 J defined 158 Johnson, W.E. 19 26 118 372 Joint assertion 18 Jolly, H.L.P. 137 Jourdain, P.E.B. 38 K defined 221 K tables 396 Kapteyn 269 Kendall, M.G. 49 81 88 96 210 239 281 326 372 Keynes, Lord 26 59 147 Knott, C.G. 326 Knowledge, vague 107 121 152 219 225 306 377 Lagrange, J.L. 376 Lange, J. 238 355 Language 19 20 32 45 372 378 391 Laplace, P.S. 14 23 29 31 34 62 102 107 133 374 389 Laplace, P.S. rule of succession 110 Latin square 215 Law of Large Numbers 52 Law, scientific 3 13 99 113 220 336 349 Le Vender, U.J.J. 389 Least squares 129 Least squares, approximations 140 173 Likelihood 29 47 99 Likelihood maximum 168 170 189 Limit of sampling ratio 53 341 345 Littlewood, J.E. 56 76 Location parameter 63 Logical product 18 25 Logical quotient 25 Logical sum 18 25 Lord Rayleigh 260 Lord Rutherford 59 Lueders, R. 70 Materialism 394 Mathematics, applied 2 3 12 Mathematics, pure 2 10 37 Maximum likelihood 168 170 189 Maximum likelihood, relation to invariance theory 169 Maxwell, J.C. 1 369 McColl, H. 26 Mean square contingency 212 Mean square contingency, deviation 92 Measures, significance tests 242 251 315 Median law 76 78 188 Median of general law 148 Median, use of 187 293 Mendelism 108 282 311 360 Mercury, perihelion of 387 Metaphysics 394 Method and material 7 9 10 388 Milne, E.A. 6 Milne-Thomson, L.M. 62 Mind, human 5 9 37 107 377 392 Mises, R. 341 345 Miss Bellamy, E.F. 324 Miss Hosiasson, J. 342 Miss Newbold, E.M. 295 Miss Pairman, E. 187 Moments 73 74 76 183 Moon, secular acceleration of 389 Moore, G.E. 17 Muirhead, J.H. 14 Multinomial law 57 90 Multiple sampling 57 Multiplicative axiom 10 56 Naive realism and idealism 46 383 Negative binomial 68 77 293 Newall, H.F. 387 Newman, M.H.A. 213 Newton 40 340 362 Neyman, J. 172 177 341 343 366 Nitrogen, density of 260 Normal equations 133 Normal law, departure from 190 Normal law, derivation 60 79 Normal law, estimation problem 120 Normal law, moments 78 Normal law, reproductive property 79 Normal law, significance tests for parameters 242 251 Normal law, test of 287 Null hypothesis 229 Numbers, introduction of 19 Nutation 278 Objectivity 11 376 Observations, rejection of 188 Ockham 315 385 Offord, A.C. 150 P integral 355 398 Paneth, F.A. 263 Parallax, negative 142 204 Parallax, stellar 300 Parameters, location and scale 63 Parameters, number admissible 100 315 Parameters, old and new 222 Parameters, orthogonal 184 223
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