Modern Mathematical Statistics

1.OVERVIEW AND DESCRIPTIVE STATISTICS. Introduction. Populations, Samples, and Processes. Pictorial and Tabular Methods in Descriptive Statistics. Measures of Location. Measures of Variability. 2.PROBABILITY. Introduction. Sample Spaces and Events. Axioms, Interpretations, and Properties of Probability. Counting Techniques. Conditional Probability. Independence. 3.DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Introduction. Random Variables. Probability Distributions for Discrete Random Variables. Expected Values of Discrete Random Variables. Moments and Moment Generating Functions. The Binomial Probability Distribution. The Hypergeometric and Negative Binomial Distributions. The Poisson Probability Distribution. 4.CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Introduction. Probability Density Functions and Cumulative Distribution Functions. Expected Values and Moment Generating Functions. The Normal Distribution. The Gamma Distribution and Its Relatives. Other Continuous Distributions. Probability Plots. Transformations of a Random Variable. 5.JOINT PROBABILITY DISTRIBUTIONS. Introduction. Jointly Distributed Random Variables. Expected Values, Covariance, and Correlation. Conditional Distributions. Transformations of Random Variables. Order Statistics. 6.STATISTICS AND SAMPLING DISTRIBUTIONS. Introduction. Statistics and Their Distributions. The Distribution of the Sample Mean. The Distribution of a Linear Combination. Distributions Based on a Normal Random Sample. Appendix. 7.POINT ESTIMATION. Introduction. Some General Concepts of Point Estimation. Methods of Point Estimation. Sufficiency. Information and Efficiency. 8.STATISTICAL INTERVALS BASED ON A SINGLE SAMPLE. Introduction. Basic Properties of Confidence Intervals. Large-Sample Confidence Intervals for a Population Mean and Proportion. Intervals Based on a Normal Population Distribution. Confidence Intervals for the Variance and Standard Deviation of a Normal Population. Bootstrap Confidence Intervals. 9.TESTS OF HYPOTHESES BASED ON A SINGLE SAMPLE. Introduction. Hypotheses and Test Procedures. Tests About a Population Mean. Tests Concerning a Population Proportion. P-Values. Some Comments on Selecting a Test Procedure. 10.INFERENCES BASED ON TWO SAMPLES. Introduction. z Tests and Confidence Intervals for a Difference between Two Population Means. The Two-Sample t Test and Confidence Interval. Analysis of Paired Data. Inferences about Two Population Proportions. Inferences about Two Population Variances. Comparisons Using the Bootstrap and Permutation Methods. 11.THE ANALYSIS OF VARIANCE. Introduction. Single-Factor ANOVA. Multiple Comparisons in ANOVA. More on Single-Factor ANOVA. Two-Factor ANOVA with Kij = 1. Two-Factor ANOVA with Kij > 1. 12.REGRESSION AND CORRELATION. Introduction. The Simple Linear and Logistic Regression Models. Estimating Model Parameters. Inferences about the Regression Coefficient O1 | n Inferences Concerning YY x* n and the Prediction of Future Y Values. Correlation. Aptness of the Model and Model Checking. Multiple Regression Analysis. Regression with Matrices. 13.GOODNESS-OF-FIT TESTS AND CATEGORICAL DATA ANALYSIS. Introduction. Goodness-of-Fit Tests When Category Probabilities Are Completely Specified. Goodness-of-Fit Tests for Composite Hypotheses. Two-Way Contingency Tables. 14.ALTERNATIVE APPROACHES TO INFERENCE. Introduction. The Wilcoxon Signed-Rank Test. The Wilcoxon Rank-Sum Test. Distribution-Free Confidence Intervals. Bayesian Methods. Sequential Methods.