Fundamentals of Probability and Statistics for Engineers

Subject IndexAverage value, see M eanAxioms of probability, 13–14Bayes’s theorem, 24–25Bernoulli trials, 161Beta distribution, 221–226, 237generalized, 225–226mean, 223, 237variance, 223, 237Bias, 265Binomial distribution, 43, 162, 182–183characteristic function, 164mean, 164, 184Poisson approximation, 182–183table, 365–366variance, 164, 184Boole’s inequality, 30Brownian motion, 106Cauchy distribution, 126Central limit theorem, 199–201Characteristic function, 98joint, 108Chebyshev inequality, 86–87Chi-squared distribution, 219–221, 236mean, 221, 236table, 371variance, 221, 236Chi-squared text, 316Coefficient of excess, 83Coefficient of skewness, 83Coefficient of variation, 81Computer software, 3, 375–377Confidence interval, 295, 296, 298, 302Confidence limit, 347Consistency, 274Correlation, 88–90perfect, 90zero, 90Correlation coefficient, 88–89Covariance, 88matrix, 93Cramér–Rao inequality, 267–270lower bound (CRLB), 269Cumulant, 101Cumula tive dist ribution function seeProbability distribution functionD 2 distribution, 327table, 372De Morgan’s laws, 11–12D ensit y function see Probab ilit y d en sit yfunctionD ist ribution function, see Probab ilit ydistribution functionEfficiency, 270asymptotic, 271Error, 316type I, 316type II, 316Estimate, 264Estimator, 265consistent, 274efficient, 270,271sufficient, 275unbiased minimum-variance, 266Event, 12Excel 2000, 3Expectation, 75–76conditional, 83–85mathematical, 75operator, 75Exponential distribution, 45, 78, 215–219,236mean, 215, 236variance, 215, 236Exponential failure law, 218Fundamentals of Probability and Statistics for Engineers T . T . Soong © 2004 J o h n W iley & So n s, L t dISBNs: 0-470-86813-9 (HB) 0-470-86814-7 (PB)TLFeBOOK