An Introduction to Probability and StatisticsThe second edition of a well-received book that was published 24 years ago and continues to sell to this day, An Introduction to Probability and Statistics is now revised to incorporate new information as well as substantial updates of existing material. |
Contents
1 Probability | 1 |
2 Random Variables and Their Probability Distributions | 40 |
3 Moments and Generating Functions | 69 |
4 Multiple Random Variables | 102 |
5 Some Special Distributions | 180 |
6 Limit Theorems | 256 |
7 Sample Moments and Their Distributions | 306 |
8 Parametric Point Estimation | 353 |
11 Confidence Estimation | 527 |
12 General Linear Hypothesis | 561 |
13 Nonparametric Statistical Inference | 598 |
References | 663 |
Frequently Used Symbols and Abbreviations | 669 |
Statistical Tables | 673 |
Answers to Selected Problems | 693 |
| 705 | |
9 NeymanPearson Theory of Testing of Hypotheses | 454 |
10 Some Further Results of Hypothesis Testing | 490 |
Common terms and phrases
absolutely continuous assume asymptotically Bayes Bayes estimator coefficient compute confidence interval consider continuous type converges Corollary defined Definition density DF F equivariant equivariant estimator EX² Example exists exponential family Find finite fo(x given H₁ hypothesis iid RVs independent RVs inequality integer invariant joint PDF Let X1 likelihood linear loss function mean method minimal normal distribution order statistics otherwise parameter PDF f(x PDF ƒ PDF PMF population probability probability space problem Proof random sample random variable real numbers reject Remark RV with PDF RVs with common sample space Section sequence of RVs Show sufficient statistic Suppose symmetric Theorem U-statistic UMP test UMVUE unbiased estimator values var(X variance write x²(n Xn be iid Y₁ σ²