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9780534929305

Introduction to Probability and Mathematical Statistics

by
  • ISBN13:

    9780534929305

  • ISBN10:

    0534929303

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 1991-11-24
  • Publisher: Cengage Learning
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Summary

Well received in its first edition, this edition gives a well developed, reliable introduction to the filed. The text gives students a strong theoretical foundation balanced with numerous applied and realistic exercises and examples. For flexibility in course contents, advanced or optional topics such as extreme-value distributions, regression and linear models, and reliability and survival distributions are included. This edition has been revised to include more theoretical discussion to provide a solid grounding in theory while giving students an idea of how the subject appliues to the real world. The text has also been revised to allow for an earlier development of properties of random variables and their distributions. Special probability distributions are placed separately in Chapter 3.

Table of Contents

Probability
1(52)
Introduction
1(1)
Notation and terminology
2(7)
Definition of probability
9(4)
Some properties of probability
13(3)
Conditional probability
16(15)
Counting techniques
31(22)
Summary
42(1)
Exercises
43(10)
Random Variables And Their Distributions
53(37)
Introduction
53(3)
Discrete random variables
56(6)
Continuous random variables
62(9)
Some properties of expected values
71(7)
Moment generating functions
78(12)
Summary
83(1)
Exercises
83(7)
Special Probability Distributions
90(46)
Introduction
90(1)
Special discrete distributions
91(18)
Special continuous distributions
109(15)
Location and scale parameters
124(12)
Summary
127(1)
Exercises
128(8)
Joint Distributions
136(35)
Introduction
136(1)
Joint discrete distributions
137(7)
Joint continuous distributions
144(5)
Independent random variables
149(4)
Conditional distributions
153(5)
Random samples
158(13)
Summary
165(1)
Exercises
165(6)
Properties of Random Variables
171(22)
Introduction
171(1)
Properties of expected values
172(5)
Correlation
177(3)
Conditional expectation
180(6)
Joint moment generating functions
186(7)
Summary
188(1)
Exercises
189(4)
Functions of Random Variables
193(38)
Introduction
193(1)
The CDF technique
194(3)
Transformation methods
197(12)
Sums of random variables
209(5)
Order statistics
214(17)
Summary
226(1)
Exercises
226(5)
Limiting Distributions
231(32)
Introduction
231(1)
Sequences of random variables
232(4)
The central limit theorem
236(4)
Approximations for the binomial distribution
240(3)
Asymptotic normal distributions
243(2)
Properties of stochastic convergence
245(2)
Additional limit theorems
247(3)
Asymptotic distributions of extreme-order statistics
250(13)
Summary
259(1)
Exercises
259(4)
Statistics And Sampling Distributions
263(25)
Introduction
263(1)
Statistics
263(4)
Sampling distributions
267(6)
The t, F, and beta distributions
273(7)
Large-sample approximations
280(8)
Summary
283(1)
Exercises
283(5)
Point Estimation
288(47)
Introduction
288(2)
Some methods of estimation
290(12)
Criteria for evaluating estimators
302(9)
Large-sample properties
311(8)
Bayes and minimax estimators
319(16)
Summary
327(1)
Exercises
328(7)
Sufficiency And Completeness
335(23)
Introduction
335(2)
Sufficient statistics
337(5)
Further properties of sufficient statistics
342(3)
Completeness and exponential class
345(13)
Summary
353(1)
Exercises
353(5)
Interval Estimation
358(31)
Introduction
358(1)
Confidence intervals
359(3)
Pivotal quantity method
362(7)
General method
369(8)
Two-sample problems
377(5)
Bayesian interval estimation
382(7)
Summary
383(1)
Exercises
384(5)
Tests Of Hypotheses
389(53)
Introduction
389(6)
Composite hypotheses
395(3)
Tests for the normal distribution
398(6)
Binomial tests
404(2)
Poisson tests
406(1)
Most powerful tests
406(5)
Uniformly most powerful tests
411(6)
Generalized likelihood ratio tests
417(9)
Conditional tests
426(2)
Sequential tests
428(14)
Summary
435(1)
Exercises
436(6)
Contingency Tables and goodness-Of-Fit
442(26)
Introduction
442(1)
One-sample binomial case
443(1)
r-Sample binomial test (completely specified H0)
444(3)
One-sample multinomial
447(1)
r-Sample multinomial
448(2)
Test for independence, r x c contingency table
450(3)
Chi-squared goodness-of-fit test
453(4)
Other goodness-of-fit tests
457(11)
Summary
461(1)
Exercises
462(6)
Nonparametric Methods
468(31)
Introduction
468(1)
One-sample sign test
469(2)
Binomial test (test on quantiles)
471(5)
Two-sample sign test
476(1)
Wilcoxon paired-sample signed-rank test
477(5)
Paired-sample randomization test
482(1)
Wilcozon and Mann-Whitney (WMW) tests
483(3)
Correlation tests-tests of independence
486(6)
Wald-Wolfowitz runs test
492(7)
Summary
494(1)
Exercises
495(4)
Regression And Linear Models
499(41)
Introduction
499(1)
Linear regression
500(1)
Simple linear regression
501(14)
General linear model
515(14)
Analysis of bivariate data
529(11)
Summary
534(1)
Exercises
535(5)
Reliability And Survival Distributions
540(47)
Introduction
540(1)
Reliability concepts
541(7)
Exponential distribution
548(12)
Weibull distribution
560(10)
Repairable systems
570(17)
Summary
579(1)
Exercises
579(8)
Appendix A Review Of Sets 587(7)
Appendix B Special Distributions 594(4)
Appendix C Tables Of Distributions 598(21)
Answers To Selected Exercises 619(19)
References 638(3)
Index 641

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