Fundamentals of Probability and Statistics for Engineers

Pascal dist ribution, see N egative binomia l
distribution
Poisson distribution, 173–176, 184
mean, 176, 184
table, 367
variance, 176, 184
Population, 259
Probability, 13
assignment, 16, 17
conditional,20–21
function, 13
measure, 13
Probability density function (pdf), 44–46
conditional,62–63
joint (jpdf), 49–51
marginal, 57
Probability distribution function (PD F ), 39–41
bivariate, 49
conditional, 61
joint (JPD F ), 49–51
marginal, 50
mixed-type, 46
Probability mass function (pmf), 41, 43
conditional, 61
joint (jpmf), 51–55
marginal, 52

Random experiment, 12
R a ndom sa mple, see Sa mple
Random variable,37–39
continuous, 38
discrete, 38
function of, 120
sum of, 145
Random vector
Random walk, 52
Range space, 120
R egression coefficient, 336
confidence interval, 347
least-square estimate, 344
test of hypothesis, 316
Relative likelihood,16–17
R eliability, 60, 218
Residual, 337
Return period, 169

Sample, 259
size, 260
value, 260
Sample mean, 97, 261
mean, 261
variance, 261

Sample moment, 263–264

Sample point, 12

Sample space, 12

Sample variance, 262–263

mean, 262

variance, 262

Schwarz inequality, 92

Set, 8–12

complement of, 9

countable (enumerable), 8

disjoint, 10

element, 8

empty, 9

finite, 8

infinite, 8

subset of, 8

uncountable (nonenumerable), 8

Set operation, 9–12

difference, 10

intersection (product), 10

union (sum), 9

Significance level, 319

Spreadsheet, 3

Standard deviation, 79–81

Statistic, 260

sufficient, 275

St atistica l independence, see

Independence

Sterling’s formula, 107

St u d en t ’s t - d ist r ib u t io n , 298–299

table, 370

Sum of random variables, 93,

145–146

characteristic function, 104–105

moment, 94

probability distribution, 106, 146

Test of hypothesis, 316

Total probability theorem, 23

Tree diagram, 27–28

Unbiasedness, 265

U niform distribution, 57, 189, 236

bivariate, 193

mean, 192, 236

variance, 192, 236

Unimodal distribution, 79

Variance, 79, 82

Venn diagram, 9

Weibull distribution, 235

Subject Index 391