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Run, 351 Runs test for randomness, 350, 361, 364 Sample, 153 Sample correlation coefficient, 268 Sample mean, 155, 163, 177, 178 Sample moments, 177 Sample point, 3 Sample size, 153 Sample space, 3, 10 countably infinite, 4 discrete, 4 finite, 4 Sample statistic, 154 Sample variance, 157, 177 Sampling, 153 Sampling distribution of means, 155, 163, 181 related theorems when population variance is known, 155 156 when population variance is not known, 159, 174 Sampling distribution, 155, 163, 166, 169, 171 of differences and sums, 157, 169 of proportions, 156, 166 of ratios of variances, 159, 174 of variances, 158, 169, 171 Sampling theory of correlation, 274, 298 Sampling theory of regression, 297 Sampling with replacement, 112, 153 Sampling without replacement, 113, 153 Scatter diagram, 265, 280 Semi-interquartile range, 84 Sign test, 348, 352 Significance of a difference between correlation coefficients, 274 Skewness, 84, 96, 97, 181 Spearman s formula for rank correlation, 352 Spearman s rank correlation coefficient, 271 Standard deviation, 77, 87 Standard error, 155 table for, 160 Standard error of estimates, 269, 287 Standard normal curve, 110 Standard normal density function, 110 Standard score, 78, 110 Standard units, 78 Standardized random variable, 78 Statistic, 154, 155 Statistical decisions, 213 Statistical hypotheses, 213 Statistical inference, 153 Statistical significance, 214 Stirling s formula, 10 Strong law of large numbers, 83 Student s t distribution, 115, 136 tests involving, 236 Subjective probability, 372, 388 t distribution, 115 tests involving, 236 Tests of hypothesis and significance, 213 264 for correlation coefficient, 274 for differences between correlation coefficients, 274 for differences of means, 217, 218, 227, 255 for differences of proportions, 217, 227, 253 involving chi-square distribution, 217, 233, 242, 257 involving F distribution, 217, 233, 257 involving the normal distribution, 214, 222, 255 involving Student s t distribution, 218, 230 for large samples, 216, 217 for means, 216, 217, 222, 255 for predicted values in linear regression, 273 for proportions, 216, 222, 255 for ratios of variances, 218 for regression coefficient in linear regression, 273 for small samples, 217 for variances, 218 Theoretical frequency, 221 Theory of runs, 350 Three-factor experiments, 329 Three-way classification, 329 Total variation, 270, 273, 315, 319 Transformed variables, 265 Translation of axes, 267 Treatment effects, 320 Treatment means, 314 Treatments, 314 Treatments and blocks, 318 Tree diagram, 8, 17 Trend pattern, 351, 362 Trend values, 301 Two-factor experiments with replications, 321, 331 Two-factor experiments, 318, 330 Two-sided tests, 214 Two-tailed tests, 214 Two-way classification, 318, 330 Type I error, 213 Type II error, 213 Unbiased estimate, 158, 195, 199 Unbiased estimator, 158, 195, 199 Unequal numbers of observations, 318 Unexplained variation, 270, 273 Uniform distribution, 113 114, 132, 133 Vague prior distribution, 373 Variance, 77, 78, 81, 87, 100 for grouped data, 161, 162 for samples, 177 of binomial distribution, 109 conditional, 82, 93, 102 of F distribution, 116 of normal distribution, 110 of Student s t distribution, 116 pooled, 218 sampling distribution of, 171 Variation: between treatments, 315 expected value, 316 explained, 289 distribution, 317 for two-factor experiments, 319 residual, 319 shortcut methods for obtaining, 315 total, 289, 315 unexplained, 292 within treatments, 315 Weak law of large numbers, 83 Weibull distribution, 118, 141 Yates s correction for continuity, 221, 242, 244, 247 Z transformation, Fischer s, 274.

Di erentiating the expression for v and setting t 0 yields dv !d A2 A1 or dt t 0 Since A1 50:0, A2 and so V0 =RC V0 49:0 !d V

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Prior and posterior odds ratios, 384 Prior probability, 373 Probability, 5 axioms of, 5 calculation, 12, 22, 23 classical approach, 5 concept of, 5 density function, 37 discrete, 34 distribution, 34, 37, 44 distributions of functions of random variables, 42 frequency approach, 5 function, 34 graph paper, 219 interpretation of correlation, 273, 295 interpretation of regression, 271, 295 joint, 39, 47, 48 of an event, 5 of failure, 108 of success, 108 surface, 40 using combinatorial analysis, 22 Product-moment formula, 270, 290 Quadratic curve, 265 Quality control charts, 219, 238 Random experiments, 3, 10 Random numbers, 154 Random sample, 154 Random variable, 34 continuous, 36 discrete, 34, 44 nondiscrete, 34 Randomized blocks, 323 Rank correlation, 271, 293, 365 Region of: acceptance, 214 nonsignificance, 214 rejection, 214 significance, 214 Regression, 265 equation, 265, 269 line, 272 plane, 269 surface, 269 Relationship: among, chi-square, F, and t distributions, 117, 139 between binomial and normal distributions, 111 between binomial and Poisson distributions, 111 between Poisson and normal distributions, 112 between estimation theory and hypothesis testing, 219 Relative (percentage) frequency distribution, 161 Reliability, 195 Repetitions, 314 Replications, 314, 321 Residual (in regression), 266 Residual variation, 319 Row means, 314 rth moment: about the mean, 78 79 about the origin, 82 central, 78 79 conditional, 82 raw, 79

The critically damped case will not be examined for the parallel RLC circuit, since it has little or no real value in circuit design. In fact, it is merely a curiosity, since it is a set of circuit constants whose response, while damped, is on the verge of oscillation.

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