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| Авторизация |
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| Spiegel M.R. — Schaum's outline of theory and problems of probability and statistics |
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| Предметный указатель |
kurtosis 85 97—99 143 183
Kurtosis of binomial distribution 109
Kurtosis of normal distribution 111
Kurtosis of Poisson distribution 112
Large samples 195 199—201
Latin squares 316 327 328
Law of Large Numbers 84 95
Law of large numbers for Bernoulli trials 109 123 124
Least-squares lines 259 260 268—274 289 292—294
Least-squares lines in terms of sample variance and covariance 261
Least-squares lines, intersection of 260 271
Least-squares method 259
Least-squares method for curves 259 265
Least-squares method for lines see "Least-squares lines"
Least-squares method for parabolas 259
Leibniz's rule for differentiating an integral 42 58 60
Levels of significance 212 221
Levels of significance, experimental or descriptive 224
Levels of significance, table of 213
Linear correlation coefficient 263 264 281—284
Linear correlation coefficient, generalization of 264
Linear correlation coefficient, product-moment formula for 263 282 293 294
Linear or mathematical model for analysis of variance 307 308 312 313
Linear relationship 258 262 284
Loaded coin 5
Logarithms, table of common 350 351
Lottery 86
Marginal density functions 45
Marginal distribution functions 45 54 55 268
Marginal frequency 219 297
Marginal frequency, totals 297
Marginal probability functions 44 53
Mathematical expectation 76 77 see
Mathematical models 7
Mathematical models for analysis of variance 307 308 312 313
Maximum likelihood estimates 198 206 207
Maxwell distribution 119
Mean 76 96 97 see
Mean deviation 85 97
Mean of a sample 157
Mean of a set of numbers 76
Mean of binomial distribution 109 123
Mean of F distribution 117
Mean of normal distribution 111
Mean of Poisson distribution 112
Mean of Student's t distribution 117
Mean, computation of for grouped data 164 165 179—183
Measurable sets 6
measures of central tendency 76 84 86 96 97
Measures of dispersion 85 96 97
Median 84 156 194 198
Median, nonuniqueness of 84 96 97
Median, sampling distribution of 162
Members or elements of sets 1
Mendel's experiments 241
MODE 84 96
Mode of beta distribution 115
Mode of F distribution 117
Molecule of ideal gas 151
Moment generating function 80 89—91 98
Moment generating function of binomial distribution 109 122 123
Moment generating function of chi-square distribution 135
Moment generating function of normal distribution 111 126 127
Moment generating function of Poisson distribution 112
Moment generating function, theorems on 80
Moment generating function, uniqueness theorem for 80
Moments 79 80 89—91 156
Moments, about the mean 79
Moments, about the origin 79
Moments, central 79
Moments, computation of for grouped data 164 165 179—183
Moments, conditional 83 94
Monotonically increasing functions 40 41 43
Multimodal distributions 84
Multinomial distribution 113 132 220 249
Multinomial expansion 113
Multinomial population 218
Multiple correlation coefficients 264 285
Multiple regression 262 278 279
Mutually exclusive events 5—7
Negative binomial distribution 118
Noncountably infinite sample spaces 4
Nondiscrete sample spaces 4
Nonlinear regression curves 264
Nonlinear relationships 258 284
Nonparametric statistics 186
Normal curve 99 see
Normal curve graph paper 217
Normal curve, areas under 124 125 345
Normal curve, standard 110 344 345
Normal distribution 109—111 124—127
Normal distribution, bivariate 118 141
Normal distribution, chi-square and 135
Normal distribution, density function for 109
Normal distribution, fitting of data by 237 238
Normal distribution, properties of 111
Normal equations for least-squares line 260 269 270 293 294
Normal equations for least-squares parabola 261 276 277
Normal equations for least-squares regression plane 262 278 279
Normal population 156
Normally distributed random variables 110
Null hypotheses 211 214
Null set 2
Observed frequency 218
OC curves 217 232—236 248
Odds 5
Ogives 164 179
One-factor experiments 306—310 316—321
One-tailed tests 213
One-way classification or one-factor experiments 306 316—321
One-way classification table 219 220
Open and closed intervals 2
Operating characteristic curves 217 232—236 248
Ordinates 49 84
Orthogonal squares 316
Overall mean 306 311
parabola 259
Parabola, least-squares 259 261 265 276 277 292 293
Parabolic curve 258
Parameters, population 156
Pascal's distribution 118
Pascal's triangle 25
Percentage frequency 163
Percentage frequency distributions 163
Percentage frequency distributions, cumulative 178
Percentage ogives 164
Percentiles or percentile values 84 85 99
Perfect linear correlation and regression 261 263
permutations 10 21—23
Point estimates 194
Poisson distribution 111 112 129 130 145
Poisson distribution, fitting of data by 239
Poisson distribution, properties of 111 112
Poisson distribution, relation of to binomial distribution 112
Poisson distribution, relation of to normal distribution 112 129
Poisson, S.D. 111
Poisson-distributed random variables 111 249
Poker 26 27 36 37
Polygon graph 163
Pooled variance 216
Population 155 158 159
Population variance, case of unknown 161 176
Population, normal 156
Population, parameters 156
Population, size 155
Power curve 234 248
Power of a test 217 234
Probabilities, assignment of 7 8
Probabilities, calculation of 15—17
Probability distributions 38 49 50
| Probability distributions of functions of random variables 46 47
Probability distributions, continuous 40 41
Probability distributions, discrete 38 39 51 52
Probability function 6 38
Probability function, marginal 44 53
Probability of causes see "Bayes' theorem or rule"
Probability, as a real-valued function 6
Probability, concept of 5
Probability, conditional 8 17—20 48
Probability, density function 41
Probability, function see "Probability function"
Probability, geometrical 48 63 64
Probability, graph 37 39
Probability, graph paper 217 237 238
Probability, some important theorems on 6 7 15
Probability, using combinatorial analysis 25—27
Probable significance 223 226 231 239
Product-moment formula for linear correlation coefficient 263 282 293 294
Proper subsets 1
Property method 1 11
Proportions, sampling distribution of 158 159 162 168—171
Quadratic curve 258
Quality control 217
Quality control charts 217 236 237
Radioactive particles 144
Random experiments 4 5 14 15
Random function see "Random variable"
Random numbers 156 183 184 241
Random numbers, table of 352
Random sample 156
Random variables 38 49 50
Random variables, binomially distributed 108
Random variables, continuous 38
Random variables, dimensionless 79
Random variables, discrete 38 49 50
Random variables, independent 45 46 52—56 63
Random variables, normally distributed 110
Random variables, Poisson-distributed 111 249
Random variables, standardized 79 89 110
Random variables, uncorrected 82
Random variables, uniformly distributed 114
Randomization, complete 315
Randomized blocks 315 316
RANGE 85 97
Range, semi-interquartile 85 97 198
Rank correlation 264 285—287 295 296
Raw data 163
Reaction times 191 201
Real line 2
Real numbers 2 12
Regression 259
Regression, coefficient 2«6 289 290
Regression, curve 259 264 265 287—289
Regression, equation 259 262
Regression, line 271
Regression, multiple 262 278 279
Regression, plane 262
Regression, probability interpretation of 265 266 287—289
Regression, sampling theory of 266 267 289 290
Regression, surfaces 262
Rejection region 212
Relative frequency 163 164
Relative frequency distribution 163 164
Relative frequency distribution, cumulative 164
Relative frequency, cumulative 164
Reliability 194
Replications 306 313—315 324—327
Residual 259
Residual or random variation 311 326
Rod graph 198
Root mean square (rms) speed 151
Roster method 1 11
Row means 306
Royal flush 36
Russell's paradox 32
Sample mean 157
Sample point 4
Sample size 155
Sample space 4 14 16
Sample statistics 156 157
Sample variance 160
Sample variance, expectation of 194 195
Samples 155
Samples, independent 159 171 196
Samples, random 156
Sampling 155
Sampling distribution 157
Sampling distribution of differences and sums 159 160 171—173
Sampling distribution of means 158 162 165—168 184
Sampling distribution of medians 162
Sampling distribution of proportions 158 159 162 168—171
Sampling distribution of ratios of variances 161 162 176 177
Sampling distribution of standard deviations 162
Sampling distribution of variances 160—162 173—176
Sampling distribution of various statistics 162
Sampling with or without replacement 113 114 155 156 165—167 186 196 200
Sampling, number 183 184
Sampling, theory of correlation and regression 266—268 289—292
Scatter 78 85 262
Scatter, diagram 258 265 273
Score sheet 177
Secretary or envelope problem 29 30 37
Semi-interquartile range 85 97 198
Series 341
Series, Taylor 80
Set operations 2 3 12 13
Set operations, on events 5
Sets 1 11—13
Sets, theorems on 12 13
Significance level 212 213 221
Significance level, experimental or descriptive 224
Significance, region of 212
Significance, tests of 211 see
Simple events 4 7
Skewed to right or left 85
skewness 85 97—99 143 156 183
Skewness of binomial distribution 109
Skewness of normal distribution 111
Skewness of Poisson distribution 112
Spearman's formula for rank correlation 264 285—287 295 296
Spearman's formula for rank correlation, derivation of 285 286
Staircase function 40
Standard deviation 78 88 89 see
Standard error 157 165 194
Standard error of estimate 262 263 279—281 284 285
Standard error of estimate in terms of variance and correlation coefficient 262 266 293 299
Standard normal curve 110
Standard normal curve, areas under 345
Standard normal curve, ordinates of 344
Standard normal density function 110
Standard score 79 110
Standard units 79
Standardized random variables 79 89 110
Statistical decisions 211
Statistical hypotheses 211
Statistical inference 155
Statistics, sample 156 157
Step function 40
Stirling's approximation to n! 11 27 342
Stochastic variable see "Random variahles"
Strong Law of Large Numbers 84 see
Student's t distribution 116 117 137 138 161 195 196 215 266 267
Student's t distribution, areas under 138 346
Student's t distribution, mean and variance of 117
Student's t distribution, relation of to chi-square and F 118 139—141
Student's t distribution, relation of to normal distribution 117
Student's t distribution, theorems on 117
subsets 1
Success, probability of 108
Sums, special 341
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