Preface 

xi  

Introduction to Probability 


1  (48) 

The History of Probability 


1  (1) 

Interpretations of Probability 


2  (3) 


5  (1) 


6  (6) 

The Definition of Probability 


12  (7) 


19  (3) 


22  (6) 


28  (7) 


35  (4) 

The Probability of a Union of Events 


39  (6) 


45  (2) 


47  (2) 


49  (48) 

The Definition of Conditional Probability 


49  (7) 


56  (10) 


66  (13) 


79  (10) 

The Gambler's Ruin Problem 


89  (4) 


93  (4) 

Random Variables and Distributions 


97  (84) 

Random Variables and Discrete Distributions 


97  (6) 


103  (6) 

The Distribution Function 


109  (9) 


118  (10) 


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) 


176  (5) 


181  (66) 

The Expectation of a Random Variable 


181  (8) 

Properties of Expectations 


189  (8) 


197  (6) 


203  (6) 


209  (5) 

Covariance and Correlation 


214  (8) 


222  (7) 


229  (7) 


236  (7) 


243  (4) 


247  (76) 


247  (1) 

The Bernoulli and Binomial Distributions 


247  (4) 

The Hypergeometric Distribution 


251  (4) 


255  (8) 

The Negative Binomial Distribution 


263  (5) 


268  (14) 

The Central Limit Theorem 


282  (9) 

The Correction for Continuity 


291  (4) 


295  (8) 


303  (6) 

The Multinomial Distribution 


309  (4) 

The Bivariate Normal Distribution 


313  (7) 


320  (3) 


323  (68) 


323  (4) 

Prior and Posterior Distributions 


327  (8) 

Conjugate Prior Distributions 


335  (11) 


346  (9) 

Maximum Likelihood Estimators 


355  (9) 

Properties of Maximum Likelihood Estimators 


364  (6) 


370  (7) 

Jointly Sufficient Statistics 


377  (6) 


383  (6) 


389  (2) 

Sampling Distributions of Estimators 


391  (58) 

The Sampling Distribution of a Statistic 


391  (2) 

The ChiSquare Distribution 


393  (4) 

Joint Distribution of the Sample Mean and Sample Variance 


397  (7) 


404  (5) 


409  (7) 

Bayesian Analysis of Samples from a Normal Distribution 


416  (11) 


427  (8) 


435  (11) 


446  (3) 


449  (86) 

Problems of Testing Hypotheses 


449  (14) 

Testing Simple Hypotheses 


463  (7) 

Uniformly Most Powerful Tests 


470  (9) 


479  (6) 


485  (13) 

Comparing the Means of Two Normal Distributions 


498  (8) 


506  (8) 


514  (13) 


527  (4) 


531  (4) 

Categorical Data and Nonparametric Methods 


535  (64) 


535  (7) 

GoodnessofFit for Composite Hypotheses 


542  (8) 


550  (6) 


556  (6) 


562  (4) 


566  (9) 


575  (12) 


587  (8) 


595  (4) 

Linear Statistical Models 


599  (100) 

The Method of Least Squares 


599  (10) 


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) 


665  (8) 


673  (10) 

The TwoWay Layout with Replications 


683  (11) 


694  (5) 


699  (70) 

Why Is Simulation Useful? 


699  (14) 

Simulating Specific Distributions 


713  (14) 


727  (8) 


735  (18) 


753  (12) 


765  (4) 
Tables 

769  (12) 
Answers to OddNumbered Exercises 

781  (20) 
References 

801  (6) 
Index 

807  