Probability and statistics

Probability and Statistics
	Title Page
	Contents
	Preface
	1 Introduction to Probability
		1.1 The History of Probability
		1.2 Interpretations of Probability
		1.3 Experiments and Events
		1.4 Set Theory
		1.5 The Definition of Probability
		1.6 Finite Sample Spaces
		1.7 Counting Methods
		1.8 Combinatorial Methods
		1.9 Multinomial Coefficients
		1.10 The Probability of a Union of Events
		1.11 Statistical Swindles
		1.12 Supplementary Exercises
	2 Conditional Probability
		2.1 The Definition of Conditional Probability
		2.2 Independent Events
		2.3 Bayes’ Theorem
		2.4 The Gambler’s Ruin Problem
		2.5 Supplementary Exercises
	3 Random Variables and Distributions
		3.1 Random Variables and Discrete Distributions
		3.2 Continuous Distributions
		3.3 The Cumulative Distribution Function
		3.4 Bivariate Distributions
		3.5 Marginal Distributions
		3.6 Conditional Distributions
		3.7 Multivariate Distributions
		3.8 Functions of a Random Variable
		3.9 Functions of Two or More Random Variables
		3.10 Markov Chains
		3.11 Supplementary Exercises
	4 Expectation
		4.1 The Expectation of a Random Variable
		4.2 Properties of Expectations
		4.3 Variance
		4.4 Moments
		4.5 The Mean and the Median
		4.6 Covariance and Correlation
		4.7 Conditional Expectation
		4.8 Utility
		4.9 Supplementary Exercises
	5 Special Distributions
		5.1 Introduction
		5.2 The Bernoulli and Binomial Distributions
		5.3 The Hypergeometric Distributions
		5.4 The Poisson Distributions
		5.5 The Negative Binomial Distributions
		5.6 The Normal Distributions
		5.7 The Gamma Distributions
		5.8 The Beta Distributions
		5.9 The Multinomial Distributions
		5.10 The Bivariate Normal Distributions
		5.11 Supplementary Exercises
	6 Large Random Samples
		6.1 Introduction
		6.2 The Law of Large Numbers
		6.3 The Central Limit Theorem
		6.4 The Correction for Continuity
		6.5 Supplementary Exercises
	7 Estimation
		7.1 Statistical Inference
		7.2 Prior and Posterior Distributions
		7.3 Conjugate Prior Distributions
		7.4 Bayes Estimators
		7.5 Maximum Likelihood Estimators
		7.6 Properties of Maximum Likelihood Estimators
		7.7 Sufficient Statistics
		7.8 Jointly Sufficient Statistics
		7.9 Improving an Estimator
		7.10 Supplementary Exercises
	8 Sampling Distributions of Estimators
		8.1 The Sampling Distribution of a Statistic
		8.2 The Chi-Square Distributions
		8.3 Joint Distribution of the Sample Mean and Sample Variance
		8.4 The t Distributions
		8.5 Confidence Intervals
		8.6 Bayesian Analysis of Samples from a Normal Distribution
		8.7 Unbiased Estimators
		8.8 Fisher Information
		8.9 Supplementary Exercises
	9 Testing Hypotheses
		9.1 Problems of Testing Hypotheses
		9.2 Testing Simple Hypotheses
		9.3 Uniformly Most Powerful Tests
		9.4 Two-Sided Alternatives
		9.5 The t Test
		9.6 Comparing the Means of Two Normal Distributions
		9.7 The F Distributions
		9.8 Bayes Test Procedures
		9.9 Foundational Issues
		9.10 Supplementary Exercises
	10 Categorical Data and Nonparametric Methods
		10.1 Tests of Goodness-of-Fit
		10.2 Goodness-of-Fit for Composite Hypotheses
		10.3 Contingency Tables
		10.4 Tests of Homogeneity
		10.5 Simpson’s Paradox
		0.6 Kolmogorov-Smirnov Tests
		10.7 Robust Estimation
		10.8 Sign and Rank Tests
		10.9 Supplementary Exercises
	11 Linear Statistical Models
		11.1 The Method of Least Squares
		11.2 Regression
		11.3 Statistical Inference in Simple Linear Regression
		11.4 Bayesian Inference in Simple Linear Regression
		11.5 The General Linear Model and Multiple Regression
		11.6 Analysis of Variance
		11.7 The Two-Way Layout
		11.8 The Two-Way Layout with Replications
		11.9 Supplementary Exercises
	12 Simulation
		12.1 What Is Simulation?
		12.2 Why Is Simulation Useful?
		12.3 Simulating Specific Distributions
		12.4 Importance Sampling
		12.5 Markov Chain Monte Carlo
		12.6 The Bootstrap
		12.7 Supplementary Exercises
	Tables
	Answers to Odd-Numbered Exercises
	References
	Index
Corrections
Instructor's Solutions Manual
	Contents
	Preface
	1 Introduction to Probability
	2 Conditional Probability
	3 Random Variables and Distributions
	4 Expectation
	5 Special Distributions
	6 Large Random Samples
	7 Estimation
	8 Sampling Distributions of Estimators
	9 Testing Hypotheses
	10 Categorical Data and Nonparametric Methods
	11 Linear Statistical Models
	12 Simulation