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when sampling from a Poisson population, 391 Probability: calculation of, 12 calculating using combinatorial analysis, 22, 23 conditional, 14 distributions, 44 geometric, 60 subjective, 388 theorems on, 11 Probability distributions: continuous, 46 discrete, 44 Probability interpretation of correlation and regression, 295 Product-moment formula, 290 Proportions, sampling distribution of , 166 Quality control charts, 238 Random experiments, 10 Random variables: conditional expectation of, 93 continuous, 46 discrete, 44 expectation of, 85 independent, 47 Randomness runs test, 361 Rank correlation, 293, 365 Regression: least-squares line of, 275 multiple, 285 probability interpretation of, 295 sampling theory of, 297 Runs test for randomness, 361 applications of, 364 Sample mean: coding formula for, 178 computation of, 177 Sample moments, computation of, 177 Sample spaces, 10 Sample variance: coding formula for, 179 computation of, 177 Sampling distribution of: difference of means, 169 mean when population variance is unknown, 174 means, 163, 181 proportions, 166 ratios of variances, 174 sum of variances, 169 variances, 171 Sampling theory of: correlation, 298 regression, 297 Scatter diagram, 280 Sign test, 352 Skewness, 96, 97, 181 Standard deviation, 87 Standard error of estimate, 287 Student s t distribution, 136 relationship to F and chi-square distributions, 139 tests involving, 236 Subjective probability, 388 Tests: of difference of means, 227 of differences of proportions, 227 involving the chi-square distribution, 233, 242 involving the F distribution, 233 involving the Student s t distribution, 230 of means using normal distributions, 222 of proportions using normal distributions, 222 Theoretical distributions, fitting of data by, 239 Three-factor experiments, 329 Three-way classification, 329 Tree diagrams, 17 Trend pattern, in runs test, 362 Trend values, 301 Two-factor experiments, 330 with replication, 331 Two-way classification, 330 Unbiased estimates, 199 Uniform distribution, 132 Variables, change of, 51, 63 Variables, random (see Random variables) Variance, 87 computation of, for samples, 177 conditional, 93 sampling distribution of, 171 Variation: explained, 289 total, 289 unexplained, 292 Weibull distribution, 141.

Mann-Whitney U test, 354 sampling distribution of, 358 Marginal density function, 58 Marginal distribution function, 48, 61 Maximum likelihood estimates, 206 for mean of normal distribution, 206 for variance of normal distribution, 207 Means: computation of, for samples, 177 sampling distribution of, 163 Measures of central tendency, 94 Measures of dispersion, 96 Median, 94 Mode, 94 Modifications for unequal number of observations, 328 Moment generating function, 88, 96 of binomial distribution, 121 of Cauchy distribution, 132 of Poisson distribution, 129 of sums of independent random variables, 89 Moments, 88 computation of, 93 conditional, 93 for samples, 177 Multinomial distribution, 131 Multiple correlation coefficient, 293 Mutually exclusive events, 13 Nonlinear equations reducible to linear equations, 282 Nonlinear relationship, 292 Normal approximation to binomial distribution, 126, 129 Normal distribution, 122 bivariate, 140 One-factor experiments, 324 One-way classification, 324 Operating characteristic curve, 234, 251 Operating characteristic function, 235 Percentiles, 96 Permutations, 18 Poisson distribution, 128 moment generating function of, 129 Power function, 235 Prior and posterior distributions, 388 when sampling from a binomial population, 390 when sampling from a normal population, 391

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In general, a coil can be represented by either a series or a parallel arrangement of circuit elements. The frequency of the applied voltage may require that one or the other be used to represent the device.

A nondiscrete random variable X is said to be absolutely continuous, or simply continuous, if its distribution function may be represented as

A voltage function and a polarity must be speci ed to completely describe a voltage source. The polarity marks, and , are placed near the conductors of the symbol that identi es the voltage source. If, for example, v 10:0 sin !t in Fig. 2-4(a), terminal A is positive with respect to B for 0 > !t > , and B is positive with respect to A for > !t > 2 for the rst cycle of the sine function.

F(x)

For example, money, length, and height are measurements using ratio scales These measurements have well-understood notions of zero: zero money, zero height, and zero length Any formula for converting from one set of units to another from centimeters to inches, for example would just use a multiplicative constant The absolute is a counting scale measure The units are obvious and well understood Counting marbles is an example of an absolute scale measure..

where the function f (x) has the properties 1. f (x)

Fig. 2-4

2. 3

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