# Probability and Statistics

• ISBN13:

• ISBN10:

## 0201524880

• Edition: 3rd
• Format: Paperback
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### Summary

The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a new chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), expanded coverage of residual analysis in linear models, and more examples using real data. Probability & Statisticswas written for a one or two semester probability and statistics course offered primarily at four-year institutions and taken mostly by sophomore and junior level students, majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus. Introduction to Probability; Conditional Probability; Random Variables and Distribution; Expectation; Special Distributions; Estimation; Sampling Distributions of Estimators; Testing Hypotheses; Categorical Data and Nonparametric Methods; Linear Statistical Models; Simulation For all readers interested in probability and statistics.

Preface xi
 Introduction to Probability
1(48)
 The History of Probability
1(1)
 Interpretations of Probability
2(3)
 Experiments and Events
5(1)
 Set Theory
6(6)
 The Definition of Probability
12(7)
 Finite Sample Spaces
19(3)
 Counting Methods
22(6)
 Combinatorial Methods
28(7)
 Multinomial Coefficients
35(4)
 The Probability of a Union of Events
39(6)
 Statistical Swindles
45(2)
 Supplementary Exercises
47(2)
 Conditional Probability
49(48)
 The Definition of Conditional Probability
49(7)
 Independent Events
56(10)
 Bayes' Theorem
66(13)
 Markov Chains
79(10)
 The Gambler's Ruin Problem
89(4)
 Supplementary Exercises
93(4)
 Random Variables and Distributions
97(84)
 Random Variables and Discrete Distributions
97(6)
 Continuous Distributions
103(6)
 The Distribution Function
109(9)
 Bivariate Distributions
118(10)
 Marginal Distributions
128(8)
 Conditional Distributions
136(10)
 Multivariate Distributions
146(12)
 Functions of a Random Variable
158(7)
 Functions of Two or More Random Variables
165(11)
 Supplementary Exercises
176(5)
 Expectation
181(66)
 The Expectation of a Random Variable
181(8)
 Properties of Expectations
189(8)
 Variance
197(6)
 Moments
203(6)
 The Mean and the Median
209(5)
 Covariance and Correlation
214(8)
 Conditional Expectation
222(7)
 The Sample Mean
229(7)
 Utility
236(7)
 Supplementary Exercises
243(4)
 Special Distributions
247(76)
 Introduction
247(1)
 The Bernoulli and Binomial Distributions
247(4)
 The Hypergeometric Distribution
251(4)
 The Poisson Distribution
255(8)
 The Negative Binomial Distribution
263(5)
 The Normal Distribution
268(14)
 The Central Limit Theorem
282(9)
 The Correction for Continuity
291(4)
 The Gamma Distribution
295(8)
 The Beta Distribution
303(6)
 The Multinomial Distribution
309(4)
 The Bivariate Normal Distribution
313(7)
 Supplementary Exercises
320(3)
 Estimation
323(68)
 Statistical Inference
323(4)
 Prior and Posterior Distributions
327(8)
 Conjugate Prior Distributions
335(11)
 Bayes Estimators
346(9)
 Maximum Likelihood Estimators
355(9)
 Properties of Maximum Likelihood Estimators
364(6)
 Sufficient Statistics
370(7)
 Jointly Sufficient Statistics
377(6)
 Improving an Estimator
383(6)
 Supplementary Exercises
389(2)
 Sampling Distributions of Estimators
391(58)
 The Sampling Distribution of a Statistic
391(2)
 The Chi-Square Distribution
393(4)
 Joint Distribution of the Sample Mean and Sample Variance
397(7)
 The t Distribution
404(5)
 Confidence Intervals
409(7)
 Bayesian Analysis of Samples from a Normal Distribution
416(11)
 Unbiased Estimators
427(8)
 Fisher Information
435(11)
 Supplementary Exercises
446(3)
 Testing Hypotheses
449(86)
 Problems of Testing Hypotheses
449(14)
 Testing Simple Hypotheses
463(7)
 Uniformly Most Powerful Tests
470(9)
 Two-Sided Alternatives
479(6)
 The t Test
485(13)
 Comparing the Means of Two Normal Distributions
498(8)
 The F Distribution
506(8)
 Bayes Test Procedures
514(13)
 Foundational Issues
527(4)
 Supplementary Exercises
531(4)
 Categorical Data and Nonparametric Methods
535(64)
 Tests of Goodness-of-Fit
535(7)
 Goodness-of-Fit for Composite Hypotheses
542(8)
 Contingency Tables
550(6)
 Tests of Homogeneity
556(6)
562(4)
 Kolmogorov-Smirnov Tests
566(9)
 Robust Estimation
575(12)
 Sign and Rank Tests
587(8)
 Supplementary Exercises
595(4)
 Linear Statistical Models
599(100)
 The Method of Least Squares
599(10)
 Regression
609(9)
 Statistical Inference in Simple Linear Regression
618(20)
 Bayesian Inference in Simple Linear Regression
638(7)
 The General Linear Model and Multiple Regression
645(20)
 Analysis of Variance
665(8)
 The Two-Way Layout
673(10)
 The Two-Way Layout with Replications
683(11)
 Supplementary Exercises
694(5)
 Simulation
699(70)
 Why Is Simulation Useful?
699(14)
 Simulating Specific Distributions
713(14)
 Importance Sampling
727(8)
 Markov Chain Monte Carlo
735(18)
 The Bootstrap
753(12)
 Supplementary Exercises
765(4)
Tables 769(12)