Theory of probability

Cover......Page 1
Title: THEORY OFPROBABILITY......Page 3
ISBN 0-19-850368-7......Page 4
PREFACE TO THE CORRECTED IMPRESSION......Page 6
PREFACE......Page 8
PREFACE TO THE FIRST El)ITION......Page 10
CONTENTS......Page 12
I FUNDAMENTAL NOTIONS......Page 14
II DIRECT PROBABILITIES......Page 70
2.1. Sampling......Page 72
2.2. The normal law of error.......Page 83
2.3. The Pearson laws4......Page 87
2.4. The negative binomial law......Page 91
2.5. Correlation.......Page 94
2.6. Distribution functions......Page 96
2.61. Characteristic functions.......Page 98
2.66. Theorems on limits......Page 106
2.7. The \\Xi ^2 distribution......Page 116
2.8. The I and z distributions.......Page 121
2.9. The specification of random noise.......Page 127
III ESTIMATION PROBLEMS......Page 130
3.2. Sampling......Page 138
3.3. The Poisson distribution.......Page 148
3.4. The normal law of error.......Page 150
3.5. The method of least squares......Page 160
3.6. The rectangular distribution.......Page 174
3.62. Reading of a scale.......Page 177
3.7. Sufficient statistics.......Page 178
3.71. The Pitman—Koopman theorem.......Page 181
3.8. The posterior probabilities that the true value, or the third observation, will lie between the first two observation......Page 183
3.9. Correlation......Page 187
3.10. Invariance theory.......Page 192
4.0. Maximum likelihood.......Page 206
4.01. Relation of maximum likelihood to invariance......Page 208
4.1. An approximation to maximum likelihoo......Page 209
4.2. Combination of estimates with different estimated  uncertainties.......Page 211
4.3. The use of expectations.......Page 213
4.31. Orthogonal parameters......Page 220
4.4. If the law of error is unknown and the observations are too few......Page 224
4.43. Grouping......Page 230
4.44. Effects of grouping: Sheppard\'s corrections......Page 233
4.5. Smoothing of observed data.......Page 236
4.6. Correction of a correlation coefficient......Page 240
4.7. Rank correlation.......Page 242
4.71. Grades and contingency.......Page 248
4.8. The estimation of an unknown and unrestricted integer......Page 251
4.9. Artificial randomization.......Page 252
5.0. General discussion......Page 258
5,01. Treatment of old parameters......Page 262
5.02. Required properties of f(a).......Page 264
5.03. Comparison of two sets of observations......Page 265
5.04. Selection of alternative hypotheses.......Page 266
5.1. Test of whether a suggested value of a chance is correct......Page 269
5.11. Simple contingency......Page 272
5.82. Comparison of samples.......Page 274
5.2. Test of whether the true value in the normal law is zero: standard error originally unknown......Page 281
5.21. Test of whether a true value is zero: a taken as known......Page 287
5.3. Generalization by invariance theory......Page 288
5.31. General approximate forms.......Page 290
5.41. Test of whether two true values are equal, standard errors supposed the same.......Page 291
5.42. Test of whether two location parameters are the same, standard errors not supposed equal.......Page 293
5.43. Test of whether a standard error has a suggested value......Page 294
5.44. Test of agreement of two estimated standard error......Page 296
5.45. Test of both the standard error and the location parameter.......Page 298
5.47. The discovery of argon.......Page 300
5.5. Comparison of a correlation coefficient with a suggested value......Page 302
5.51. Comparison of correlations......Page 306
5.6. The intraclass correlation coefficient.......Page 308
5.63. Suspiciously close agreement. T......Page 320
5.7. Test of the normal Jaw of erro......Page 327
5.8. Test for independence In rare events.......Page 332
5.9. Introduction of new functions.......Page 335
5.92. Allowance for old functions.......Page 338
5.93. Two Sets of observations relevant to the same parameter.......Page 339
5.94. Continuous departure from a uniform distribution of chance.......Page 341
6.0. CombinatIon of tests.......Page 345
6.1. Several new parameters often arise for consideration simultaneously......Page 353
6.2. Two new parameters considered simultaneously......Page 356
6.23. Grouping......Page 368
6.3. Partial and serial correlation.......Page 369
6.4. Contingency affecting only diagonal elements......Page 373
6.5. Deduction as an approximation......Page 378
VII FREQUENCY DEFINITIONS AND DIRECTMETHODS......Page 382
VIII GENERAL QUESTIONS......Page 414
APPENDIX A: MATHEMATICAL THEOREMS......Page 438
A.31. Inversion of the order of integration......Page 440
A.4l. Abel\'s lemma.......Page 441
A.42. Watson\'s lemma......Page 442
APPENDIX B: TABLES OF K......Page 445
Analysis for periodicities......Page 455
Autocorrelation......Page 463
INDEX......Page 468
Back Cover......Page 473