Fundamentals of Probability and Statistics for Engineers

Extreme-value distribution, 226,
type I, 228, 237
type II, 233, 237
type III,234, 237

F a ilure rate, see H a za rd function
F isher–N eyma n fact oriza tion criterion, 275
Frequency diagram, 248
Function of random variables,119, 137
moments, 134
probability distributions, 120

G amma distribution, 212–215, 236
mean, 213, 236
variance, 213, 236
Gaus–Markov theorem, 345
G a ussian dist ribution, see N ormal
distribution
G eometric distribution, 167, 184
mean, 168, 184
variance, 168, 184
G umbel’s extreme value, 228
distribution, 228

Hazard function, 218
Histogram, 248
cumulative, 327
H ypergeometric distribution, 167, 184
mean, 184
variance, 184
H ypothesis t esting, see Test of hypothesis

Independence,19–20
mutual, 18
Interarrival time, 215

Jacobian, 149

Kolmogorov–Smirnov test, 327

Law of large numbers, 96
Least-square estimator, 354–355
covariance, 356
linear unbiased minimum variance, 344
mean, 355
variance, 355
Likelihood equation, 288
Likelihood function, 288
Linear regression, 335
multiple, 354
other models, 357
simple, 335
variance, 343

Lognormal distribution,209–212, 236

mean, 211, 236

variance, 211, 236

M acLaurin series, 99

Markovian property, 27

Markov’s inequality, 115

M a ss function, see Probabilit y m a s s f u n ct io n

Maximum likelihood estimate, 288

Maximum likelihood estimator,288–289

consistency, 289

efficiency, 289

invariance property, 290

M ean, 76–77

conditional, 84

Median, 76

Mode, 78

M oment, 76, 78

central, 79

joint, 87

joint central, 87

Moment estimate, 278

M oment estimator (M E), 278–280

combined, 284

consistency, 279

M oment-generating function, 112, 117

M ultinomial distribution, 172, 184

covariance, 173

mean, 173, 184

variance, 173, 184

M utual exclusiveness, 13

N egative binomial distribution, 169, 184

mean, 171, 184

variance, 171, 184

N ormal distribution, 107, 196–199, 236

bivariate, 111

characteristic function, 198

mean, 198, 236

multivariate, 205

standardized, 201

table, 369

variance, 198, 236

Normal equation, 338

Nuisance parameter, 284

Parameter estimation, 259

interval estimation, 294–295

maximum likelihood method, 287

moment method, 278

point estimation, 277

390 Subject Index