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Spiegel M.R. — Schaum's outline of theory and problems of probability and statistics
Spiegel M.R. — Schaum's outline of theory and problems of probability and statistics



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Название: Schaum's outline of theory and problems of probability and statistics

Автор: Spiegel M.R.

Аннотация:

This book gives theory and solved problems for a combined course in probability and mathematical statistics. A calculus background is employed. The first half of the book itself serves as a supplement to the study of probability.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 372

Добавлена в каталог: 10.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A posteriori approach to probability      6
A priori approach to probability      5
Acceptance, region of      213
Aggregate      1 see
Algebra of events      5
Alternative hypotheses      211
Analysis of variance      306—338
Analysis of variance for one-factor experiments      306—310 316—321
Analysis of variance for three-factor experiments      332 333
Analysis of variance for two-factor experiments      312—315
Analysis of variance, shortcut formulas in      307 311 317 319 320 324
Analysis of variance, tables      309 313 314 319 323
Analysis of variance, unequal numbers of observations in      310 321 322
Approximating curves      258 259
Arithmetic mean      76 84 see
Associative laws for convolutions      47
Associative laws for sets      3
Asymptotically normal random variables      111 158 161
Axes, translation of      260
Axiomatic approach to probability      6
Axioms of probability      6
Bar chart or graph      39 49
Bayes' theorem or rule      9 20 21
Bernoulli distribution      see "Binomial distribution"
Bernoulli trials      108 118
Bernoulli trials, law of large numbers for      109 123 124
Bernoulli, James      108
Bernoulli-distributed random variables      108
Best-fitting curves or lines      259
Beta distribution      115 134 135
beta function      115 342
Beta-distributed random variables      115
Biased estimates      194 see
Bimodal distribution      84
Binomial coefficients      11 25
Binomial distribution      108 109 119—123
Binomial distribution, fitting of data by      237
Binomial distribution, negative-      118
Binomial distribution, normal approximation to      127 128 168 169
Binomial distribution, Poisson approximation to      129
Binomial distribution, properties of      108 109
Binomial distribution, relation of to normal distribution      112 127 128
Binomial distribution, relation of to Poisson distribution      112
Binomial expansion      25 108
Binomial population      156 158 196
Binomially distributed random variables      108
Birthday problem      30 31
Bivariate frequency distributions and tables      297
Bivariate normal distribution      118 141
Block effects      312
BLOCKS      310 311
Blocks, randomized      315 316
Boltzmann's constant      151
Bose — Einstein statistics      36
Bridge      36 37
Buffon's Needle Problem      67 68
Categories      163
Cauchy distribution      114 115 133 134
Cauchy-distributed random variables      114 115
Cell frequency      219 297 298
cells      219 297
Central limit theorem      112 113 130 131 158 260
Central limit theorem for binomially distributed random variables      130 131
Central Limit Theorem, proof of      131
Central moments      79
Centroid or center of gravity of data      260
Chance      5
Change of variables      46 47 56—60
Change of variables for continuous case      46 47
Change of variables for discrete case      46
Characteristic function      80 81 91 92 98 99
Characteristic function of binomial distribution      109
Characteristic function of normal distribution      111
Characteristic function of Poisson distribution      112
Characteristic function, theorems on      81
Characteristic function, uniqueness theorem for      81
Chebyshev's inequality      83 84 94 95
Chi-square distributed random variables      116
Chi-square distributed random variables, relation with t and F distributions      118 139—141
Chi-square distribution      113 116 117 135—137 197 216
Chi-square distribution, areas under      136 347
Chi-square distribution, as special case of gamma distribution      116
Chi-square distribution, relation of to normal distribution      136
Chi-square distribution, theorems on      116
Chi-square test for goodness of fit      218 219 243
class      1 see
Class boundaries      163 177
Class interval      163 177 297
Class mark      163 164 177
Classes and class frequencies      163 164 177 297
Classical approach to probability      5 6
Coding methods and formulas      164 165 180—184 297
Collection      1 see
Combinations      10 11 23 24
Combinatorial analysis      9 21
Combinatorial analysis, probability using      25—27
Commutative laws for convolutions      47 61
Commutative laws for sets      3
Complement of a set      3
Complementary error function      343
Complete randomization      315
complex numbers      2
Conditional distributions      48 61—63
Conditional expectation      83 94 265
Conditional moments      83 94
Conditional probability      8 17—20
Conditional probability, function      48
Conditional probability, theorems on      8
Confidence coefficients      195
confidence intervals      194—206
Confidence intervals for differences and sums      196 197 199 203 204
Confidence intervals for means      195 196—202
Confidence intervals for proportions      196 202 203
Confidence intervals for variance ratios      197 198 205 206
Confidence intervals for variances      197 204 206
Confidence levels      195
Confidence limits      195
Contingency tables      219 220 243—246
Contingency, coefficient of      220 246 247
Continuous from the right      40
Continuous probability distributions      40 41
Continuous random variables      38
Continuous sample spaces      4
control charts      217
Control group      227 230
Convolutions      47 60 61
Correlation      258—305
Correlation coefficient      82 83 92—94 100 118 263 264 281—284
Correlation coefficient for grouped data      297
Correlation coefficient, generalized      264 284 286
Correlation coefficient, multiple      264 285
Correlation coefficient, population      265-267
Correlation coefficient, sample      261
Correlation coefficient, tests of hypotheses and significance for      267 268
Correlation, independence and      268
Correlation, probability interpretation of      266 287—289
Correlation, rank      264 285—287 295 296
Correlation, sampling theory of      267 268 290—292
Correlation, table      297
Countably infinite sample spaces      4
Counting, fundamental principle of      9 21
Covariance      81 82 92—94
Covariance, theorems on      82
Critical region      212 213
Critical values      195
Cumulative distribution function      39 see
Cumulative frequency distributions      164 178 179
Cumulative frequency polygon      179
Curve fitting      258 265 see
De Morgan's laws      3 13
Deciles      85
Decision, rules of      211 213 221—226 248
Degrees of freedom      116 117 219 220 309 312
Degrees of freedom, additivity of for chi-square distribution      116 135
Density function      41
Density function of sums of random variables      47
Density function, graphical interpretation of      42 43
Density function, joint      44 63 54
Density function, marginal      45
Dependent random variables      see "Independent random variables"
dependent variables      259 262 268 269
Design of experiments      315 316
Determination, coefficient of      263 282
Deviation      259
Deviation, standard      see "Standard deviation"
Difference of sets      3
Dimensionless random variables      79
Dimensions or units      78
Discrete probability distributions      38 39 51 52
Discrete random variables      38 49 60
Discrete sample spaces      4
Disjoint sets      3 5
dispersion      78 85 97
Distribution functions      39
Distribution functions for continuous random variables      41 42
Distribution functions for discrete random variables      39 40 50 51
Distribution functions, conditional      48 61—63
Distribution functions, joint      44 45 55
Distribution functions, marginal      45 54 55 268
Distributive law for convolutions      47
Distributive law for sets      3 13
Duality, principle of      3
E.S.P.      223 224
Einstein — Bose statistics      see "Bose — Einstein statistics"
Elementary events      4 7
Elements or members of sets      1
Empirical probability      6 164
Empirical probability, distributions      164
Empty or null set      2
Envelope problem      29 30 37
Equal sets      1
Equally likely ways      5 6
Error function      110
Error function, complementary      343
Error or residual      259 308
Estimate, standard error of      see "Standard error of estimate"
estimates      156 157 194—210
Estimates, efficient      194 198 199
Estimates, unbiased      see "Unbiased estimate"
Estimation      194—210 259
Euler's formulas      92 341
Events      4 5 14 15
Exact sampling theory      161 195 196
Expectation      76 77 86—88
Expectation of functions of random variables      77
Expectation, conditional      83 94 265
Expectation, definition of      77
Expectation, theorems on      77
Experimental design      315 316
Experiments, random      4 5 14 15
Explained variation      263 266 281 282 284 285
Exponential distribution      119
Exponential values, table of      352
Extrasensory perception      see "E.S.P."
F distribution      117 118 138 139 161 197 198 216 309
F distribution, mean and variance of      117
F distribution, mode of      117
F distribution, percentile values of      348 349
F distribution, relationship with chi-square and t      118 139—141
F distribution, theorems on      117 118
Factorial function      342
Factorial n      10
Factorial n, Stirling's approximation to      11 27 342
Failure, probability of      108
Fair coin      5
Fermi — Dirac statistics      37
Fiducial limits      195 see
Finite population      155 158 159
Finite sample space      4
Fisher's Z transformation      267
Fisher, R. A.      117 198 267 306
Fitting of data by theoretical distributions      217 237—239
Fourier integrals      81 98
Fourier series      81 98
Fourier transforms      81
Frequency approach to probability      6
Frequency distributions      163 177—179
Frequency distributions, cumulative      164 178 179
Frequency distributions, relative      163 164
Frequency polygon      163 177 178
Frequency polygon, cumulative      179
frequency tables      163 see
Full house      36
Gamma distribution      115 116 134
Gamma function      115 341 342
Gamma function, recurrence formula for      342
Gamma function, Stirling's asymptotic formula for      342
Gamma-distributed random variables      115
Gaussian distribution      109 see
Geiger counter      144
Geometric distribution      118 142
Geometric distribution, relationship of with negative binomial      118
Geometrical probability      48 63 64
Goodness of fit      217 238 243 259
Goodness of fit, chi-square test for      218 219 243
Graeco-latin squares      316 328 330
Grand mean      306 311 312
Grand total      44
Group means      306
Half open or half closed intervals      2
Heights of fathers and eldest sons      273 274 286 287 289 290
Heredity      241
Highly significant      224 225
histogram      39 49 163 177 178
Hypergeometric distribution      113 132 133
Hypergeometric distribution, mean and variance of      113 114
Hypergeometric distribution, relation of to binomial distribution      113
Hypotheses, tests of      211 see
I.Q.      230
Ideal gas      151
Impossible event      5 6
Inclusion symbols      3
Independent events      9 17—20 45
Independent random variables      45 46 52—56 63
Independent samples      159 171 196
Independent variable      259 262 269 270
Inefficient estimates      194
Inference, statistical      155
Infinite population      155 158
Integrals, special      342 343
Intelligence quotient      230
Interaction effects      314 326
intercept      260
Intersection of sets      3
Interval estimates      194
Invariance under transformation      260 264 272
Inverse Fourier transform      81
Inversion formula      81
Jacobian      46 47 56 58 59
Joint density function      44 53 54
Joint distribution function      44 45 55
Joint distribution function for continuous random variables      45
Joint distribution function for discrete random variables      44
Joint distributions      43—45 52—56
Joint distributions, continuous      44
Joint distributions, discrete      43 44
Joint distributions, variance for      81 82
Joint probability function      43 44
Joint probability table      43
Kelvin temperature      151
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