Cengage Learning A Course in Probability and Statistics

Product Description This author's modern approach is intended primarily for honors undergraduates or undergraduates with a good math background taking a mathematical statistics or statistical inference course. The author takes a finite-dimensional functional modeling viewpoint (in contrast to the conventional parametric approach) to strengthen the connection between statistical theory and statistical methodology. Review 1. RANDOM VARIABLES AND THEIR DISTRIBUTION Introduction / Sample Distributions / Distributions / Random Variables / Probability Functions and Density Functions / Distribution Functions and Quantiles / Univariate Transformations / Independence 2. EXPECTATION Introduction / Properties of Expectation / Variance / Weak Law of Large Numbers Simulation and the Monte Carlo Method 3. SPECIAL CONTINUOUS MODELS Gamma and Beta Distributions / The Normal Distribution / Normal Approximation and the Central Limit Theorem 4. SPECIAL DISCRETE MODELS Combinatorics / The Binomial Distribution / The Multinomial Distribution / The Poisson Distribution / The Poisson Process 5. DEPENDENCE Covariance, Linear Prediction, and Correlation / Multivariate Expectation / Covariance and Variance - Covariance Matrices / Multiple Linear Prediction / Multivariate Density Function / Invertible Transformations / The Multivariate Normal Distribution 6. CONDITIONAL DISTRIBUTIONS Sampling Without Replacement / Hypergeometric Distribution / Conditional Density Functions / Conditional Expectation / Prediction / Conditioning and the Multivariate Normal Distribution / Random Parameters 7. NORMAL MODELS Introduction / Chi-Square, t, and F Distribution / Confidence Intervals / The t Test of an Inequality / The t Test of an Equality 8. THE F TEST Introduction to Linear Regression / The Method of Least Squares / Factorial Experiments / Input-Response and Experimental Models 9. LINEAR ANALYSIS Linear Spaces / Identifiability / Saturated Spaces / Inner Products / Orthogonal Projections / Normal Equations 10. LINEAR REGRESSION Least-Square Estimation / Sums of Squares / Distribution Theory / sugar Beet Experiment / Lube Oil Experiment / The t Test / Submodels / The F Test 11. ORTHOGONAL ARRAYS Main Effects / Interactions / Experiments with Factors Having Three Levels / Randomization, Blocking, and Covariates 12. BINOMIAL AND POISSON MODELS Nominal Confidence Intervals and Tests / Exact P-values / One-Parameter Exponential Families 13. LOGISTIC REGRESSION AND POISSON REGRESSION Input-Response and Experimental Models / Maximum-Likelihood Estimation / Existence and Uniqueness of the Maximum-Likelihood Estimate / Interactively Reweighted Least-Squares Method / Normal Approximation / The Likelihood-Ratio Test / APPENDICES: A. PROPERTIES OF VECTORS AND MATRICES / B. SUMMARY OF PROBABILITY / C. SUMMARY OF STATISTICS / D. HINTS AND ANSWERS / E. TABLES / INDEX