Page 673 - Probability and Statistical Inference

650 Index

Applications 14-15, 53, 478-479 Comparing variances
False negative 15 528-529
False positive 15 Correlation coefficient
Posterior probability 14 525-528
Prior probability 14 Bonferroni inequality 52
Bayes test of hypothesis 493-494 Applications 157, 451-471
Behrens-Fisher problem 534, 579,v586 Borel sigma-algebra; see Borel
Fixed-width confidence sigma-field
interval 586-589 Borel sigma-field 6, 51
Test for means 534-535 Sample space 6
Two-stage sampling 586 Sets 3, 4, 51, 52
Bernoulli distribution 33, 35, 64 Bounded risk 579, 581-582
Moments 71, 72 C
Bernstein-Chernoff inequality 146
Best linear unbiased estimator Calculus reviews 28
(BLUE); see Unbiased estimator Extrema of a function
Beta distribution 48, 480-483 Maximum 31
Beta function 31 Minimum 31
Beta integral 31 Two variables 31, 32
Bias of an estimator 351 Integral
Binomial distribution 33, 35, 37, Beta function 31
59-60 Beta integral 31
Factorial moments 97 By parts 32
Moment generating function Dominated convergence
80-81 theorem 274
Moments 72, 73 Fubini’s Theorem 502
Normal approximation 277 Gamma function 30
Recursive formula 60 Gamma integral 30
Reproductive property 180 Interchanging derivative and
Binomial Theorem 17 integral 502
Applications 17-18, 54, 72, 80 Monotone convergence
Bivariate normal distribution 131- theorem 71, 92, 274
138, 169-170, 204-206, 217- Jacobian of transformation
217, 522, 535-536 193-195
Conditional distributions 134 L’Hôpital’s rule 32
Conditional means 134 Leibnitz’s rule 29
Conditional variances 134 Triangular inequality 32
Density function 131, 214 Cauchy distribution 47
Independence 139-141 Tail comparison with normal
Marginal distributions 131-133 distribution 47
Multivariate normal Cauchy-Schwarz inequality 149
Applications 122, 150-151,
distribution 212-214 156-157, 174-175, 368
Regression 218 Central absolute moment inequality
Reproductive property 216-218 159
Test procedures Applications 158
Comparing means 522-525 Central limit theorem (CLT) 242,