Preface 

xi  


1  (34) 


1  (1) 


2  (2) 


4  (2) 

Computing Probabilities: Counting Methods 


6  (10) 

The Multiplication Principle 


7  (2) 

Permutations and Combinations 


9  (7) 


16  (7) 


23  (3) 


26  (1) 


26  (9) 


35  (36) 

Discrete Random Variables 


35  (12) 

Bernoulli Random Variables 


37  (1) 

The Binomial Distribution 


38  (2) 

The Geometric and Negative Binomial Distributions 


40  (2) 

The Hypergeometric Distribution 


42  (1) 


42  (5) 

Continuous Random Variables 


47  (11) 


50  (3) 


53  (1) 


54  (4) 


58  (1) 

Functions of a Random Variable 


58  (6) 


64  (1) 


64  (7) 


71  (45) 


71  (1) 

Discrete Random Variables 


72  (3) 

Continuous Random Variables 


75  (9) 

Independent Random Variables 


84  (3) 

Conditional Distributions 


87  (9) 


87  (1) 


88  (8) 

Functions of Jointly Distributed Random Variables 


96  (8) 


96  (3) 


99  (5) 

Extrema and Order Statistics 


104  (3) 


107  (9) 


116  (61) 

The Expected Value of a Random Variable 


116  (14) 

Expectations of Functions of Random Variables 


121  (3) 

Expectations of Linear Combinations of Random Variables 


124  (6) 

Variance and Standard Deviation 


130  (8) 

A Model for Measurement Error 


135  (3) 

Covariance and Correlation 


138  (9) 

Conditional Expectation and Prediction 


147  (8) 


147  (5) 


152  (3) 

The MomentGenerating Function 


155  (6) 


161  (5) 


166  (11) 


177  (15) 


177  (1) 


177  (4) 

Convergence in Distribution and the Central Limit Theorem 


181  (7) 


188  (4) 

Distributions Derived from the Normal Distribution 


192  (7) 


192  (1) 

Χ2, t, and F Distributions 


192  (3) 

The Sample Mean and the Sample Variance 


195  (3) 


198  (1) 


199  (56) 


199  (1) 


200  (2) 


202  (18) 

The Expectation and Variance of the Sample Mean 


203  (7) 

Estimation of the Population Variance 


210  (4) 

The Normal Approximation to the Sampling Distribution of X 


214  (6) 


220  (7) 

Stratified Random Sampling 


227  (11) 

Introduction and Notation 


227  (1) 

Properties of Stratified Estimates 


228  (4) 


232  (6) 


238  (1) 


239  (16) 

Estimation of Parameters and Fitting of Probability Distributions 


255  (74) 


255  (1) 

Fitting the Poisson Distribution to Emissions of Alpha Particles 


255  (2) 


257  (3) 


260  (7) 

The Method of Maximum Likelihood 


267  (18) 

Maximum Likelihood Estimates of Multinomial Cell Probabilities 


272  (2) 

Large Sample Theory for Maximum Likelihood Estimates 


274  (5) 

Confidence Intervals from Maximum Likelihood Estimates 


279  (6) 

The Bayesian Approach to Parameter Estimation 


285  (13) 

Further Remarks on Priors 


294  (2) 

Large Sample Normal Approximation to the Posterior 


296  (1) 


297  (1) 

Efficiency and the CramerRao Lower Bound 


298  (7) 

An Example: The Negative Binomial Distribution 


302  (3) 


305  (6) 


306  (4) 

The RaoBlackwell Theorem 


310  (1) 


311  (1) 


312  (17) 

Testing Hypotheses and Assessing Goodness of Fit 


329  (48) 


329  (2) 

The NeymanPearson Paradigm 


331  (6) 

Specification of the Significance Level and the Concept of a pvalue 


334  (1) 


335  (1) 

Uniformly Most Powerful Tests 


336  (1) 

The Duality of Confidence Intervals and Hypothesis Tests 


337  (2) 

Generalized Likelihood Ratio Tests 


339  (2) 

Likelihood Ratio Tests for the Multinomial Distribution 


341  (6) 

The Poisson Dispersion Test 


347  (2) 


349  (3) 


352  (6) 


358  (3) 


361  (1) 


362  (15) 


377  (43) 


377  (1) 

Methods Based on the Cumulative Distribution Function 


378  (11) 

The Empirical Cumulative Distribution Function 


378  (2) 


380  (5) 


385  (4) 

Histograms, Density Curves, and StemandLeaf Plots 


389  (3) 


392  (9) 


393  (2) 


395  (2) 


397  (1) 


397  (1) 

Comparison of Location Estimates 


398  (1) 

Estimating Variability of Location Estimates by the Bootstrap 


399  (2) 


401  (1) 


402  (2) 

Exploring Relationships with Scatterplots 


404  (3) 


407  (1) 


408  (12) 


420  (57) 


420  (1) 

Comparing Two Independent Samples 


421  (23) 

Methods Based on the Normal Distribution 


421  (12) 


433  (2) 

A Nonparametric MethodThe MannWhitney Test 


435  (8) 


443  (1) 


444  (8) 

Methods Based on the Normal Distribution 


446  (2) 

A Nonparametric MethodThe Signed Rank Test 


448  (2) 

An ExampleMeasuring Mercury Levels in Fish 


450  (2) 


452  (7) 


452  (1) 


453  (1) 

The Lanarkshire Milk Experiment 


453  (1) 


454  (1) 


455  (1) 

Further Remarks on Randomization 


456  (1) 

Observational Studies, Confounding, and Bias in Graduate Admissions 


457  (1) 


458  (1) 


459  (1) 


459  (18) 


477  (37) 


477  (1) 


477  (12) 

Normal Theory; the F Test 


478  (7) 

The Problem of Multiple Comparisons 


485  (3) 

A Nonparametric MethodThe KruskalWallis Test 


488  (1) 


489  (15) 


489  (3) 

Normal Theory for the TwoWay Layout 


492  (8) 


500  (3) 

A Nonparametric MethodFriedman's Test 


503  (1) 


504  (1) 


505  (9) 

The Analysis of Categorical Data 


514  (28) 


514  (1) 


514  (2) 

The ChiSquare Test of Homogeneity 


516  (4) 

The ChiSquare Test of Independence 


520  (3) 


523  (3) 


526  (4) 


530  (1) 


530  (12) 


542  


542  (5) 


547  (17) 

Statistical Properties of the Estimated Slope and Intercept 


547  (3) 


550  (10) 

Correlation and Regression 


560  (4) 

The Matrix Approach to Linear Least Squares 


564  (3) 

Statistical Properties of Least Squares Estimates 


567  (13) 

VectorValued Random Variables 


567  (6) 

Mean and Covariance of Least Squares Estimates 


573  (2) 


575  (1) 

Residuals and Standardized Residuals 


576  (1) 


577  (3) 

Multiple Linear RegressionAn Example 


580  (5) 

Conditional Inference, Unconditional Inference, and the Bootstrap 


585  (2) 


587  (4) 


591  (1) 


591  
Appendix A Common Distributions 

1  (3) 
Appendix B Tables 

4  (21) 
Bibliography 

25  (7) 
Answers to Selected Problems 

32  (16) 
Author Index 

48  (3) 
Applications Index 

51  (3) 
Subject Index 

54  