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