Introduction to Probability and Mathematical Statistics

by Bain,Lee J.

• ISBN13: 9780534929305
• ISBN10: 0534929303
• Edition: 2nd
• Format: Hardcover
• Copyright: 1991-11-24
• Publisher: Cengage Learning

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