Modern Mathematical Statistics with Applications

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