Fundamentals of Probability and Statistics for Engineers

SUBJECT INDEX

Average value, see M ean
Axioms of probability,13–14

Bayes’s theorem, 24–25
Bernoulli trials, 161
Beta distribution, 221–226, 237
generalized, 225–226
mean, 223, 237
variance, 223, 237
Bias, 265
Binomial distribution, 43, 162, 182–183
characteristic function, 164
mean, 164, 184
Poisson approximation,182–183
table, 365–366
variance, 164, 184
Boole’s inequality, 30
Brownian motion, 106

Cauchy distribution, 126
Central limit theorem, 199–201
Characteristic function, 98
joint, 108
Chebyshev inequality, 86–87
Chi-squared distribution, 219–221, 236
mean, 221, 236
table, 371
variance, 221, 236
Chi-squared text, 316
Coefficient of excess, 83
Coefficient of skewness, 83
Coefficient of variation, 81
Computer software, 3, 375–377
Confidence interval, 295, 296, 298, 302
Confidence limit, 347
Consistency, 274
Correlation,88–90
perfect, 90
zero, 90

Correlation coefficient,88–89

Covariance, 88

matrix, 93

Crame ́r–R ao inequality, 267–270

lower bound (CRLB), 269

Cumulant, 101

Cumula tive dist ribution function see

Probability distribution function

D 2 distribution, 327

table, 372

D e M organ’s laws, 11–12

D ensit y function see Probabilit y d en sit y

function

D ist ribution function, see Probabilit y

distribution function

Efficiency, 270

asymptotic, 271

Error, 316

type I, 316

type II, 316

Estimate, 264

Estimator, 265

consistent, 274

efficient, 270,271

sufficient, 275

unbiased minimum-variance, 266

Event, 12

Excel 2000, 3

Expectation, 75–76

conditional,83–85

mathematical, 75

operator, 75

Exponential distribution, 45, 78,215–219,

236

mean, 215, 236

variance, 215, 236

Exponential failure law, 218

T. T. Soong  2004 J o h n W iley & So n s, L t d
ISBN s: 0-470-86813-9 (H B) 0-470-86814-7 (PB)

Fundamentals of Probability and Statistics for Engineers