This is the first half of a text for a two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the second. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "interesting but not essential" (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "INE". We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.
Author(s): Hung T. Nguyen, Gerald S. Rogers (auth.)
Series: Springer Texts in Statistics
Edition: 1
Publisher: Springer-Verlag New York
Year: 1989
Language: English
Pages: 432
Tags: Statistics, general
Front Matter....Pages i-x
Front Matter....Pages 1-1
Relative Frequency....Pages 3-10
Sample Spaces....Pages 11-18
Some Rules About Sets....Pages 19-26
The Counting Function for Finite Sets....Pages 27-35
Probability on Finite Sample Spaces....Pages 36-42
Ordered Selections....Pages 43-48
Unordered selections....Pages 49-56
Some Uniform Probability Spaces....Pages 57-62
Conditional Probability/Independence....Pages 63-71
Bayes’ Rule....Pages 72-76
Random Variables....Pages 77-83
Expectation....Pages 84-92
A Hypergeometric Distribution....Pages 93-98
Sampling and Simulation....Pages 99-103
Testing Simple Hypotheses....Pages 104-114
An Acceptance Sampling Plan....Pages 115-122
The Binomial Distribution....Pages 123-139
Matching and Catching....Pages 140-149
Confidence Intervals for a Bernoulli θ....Pages 150-165
The Poisson Distribution....Pages 166-176
Front Matter....Pages 1-1
The Negative Binomial Distribution....Pages 177-183
Front Matter....Pages 184-185
Some Set Theory....Pages 186-193
Basic Probability Theory....Pages 194-200
The Cumulative Distribution Function....Pages 201-207
Some Continuous CDFs....Pages 208-215
The Normal Distribution....Pages 216-225
Some Algebra of Random Variables....Pages 226-232
Convergence of Sequences of Random Variables....Pages 233-240
Convergence Almost Surely and in Probability....Pages 241-248
Integration — I....Pages 249-255
Integration II....Pages 256-265
Theorems for Expectation....Pages 266-274
Stieltjes Integrals....Pages 275-284
Product Measures and Integrals....Pages 285-291
Front Matter....Pages 292-293
Joint Distributions: Discrete....Pages 294-302
Conditional Distributions: Discrete....Pages 303-312
Joint Distributions: Continuous....Pages 313-321
Conditional Distributions: Continuous....Pages 322-330
Expectation-Examples....Pages 331-339
Convergence in Mean, in Distribution....Pages 340-348
Front Matter....Pages 292-293
Other Relations in Modes of Convergence....Pages 349-357
Laws of Large Numbers....Pages 358-365
Convergence of Sequences of Distribution Functions....Pages 366-372
Convergence of Sequences of Integrals....Pages 373-379
On the Sum of Random Variables....Pages 380-387
Characteristic Functions —I....Pages 388-397
Characteristic Functions–II....Pages 398-405
Convergence of Sequences of Characteristic Functions....Pages 406-414
Central Limit Theorems....Pages 415-424
Back Matter....Pages 425-432
