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An Introduction to Mathematical Statistics and Its Applications
ISBN: 9780134871745 | 013487174X
Format: HardcoverPublisher: Pearson College Div
Pub. Date: 1/1/1986
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This successful, calculus-based probability and statistics text includes real world applications used to motivate discussion. Appropriate for two-semester courses. Revision coming August of '99.
| Introduction | |
| A Brief History | |
| Some Examples | |
| A Chapter Summary | |
| Probability | |
| Sample Spaces and the Algebra of Sets | |
| The Probability Function | |
| Discrete Probability Functions | |
| Continuous Probability Functions | |
| Conditional Probability | |
| Independence | |
| Repeated Ind... MORE | |
| Combinatorics | |
| Combinatorial Probability | |
| Random Variables | |
| The Probability Density Function | |
| The Hypergeometric and Binomial Distributions | |
| The Cumulative Distribution Function | |
| Joint Densities | |
| Independent Random Variables | |
| Combining and Transforming Random Variables | |
| Order Statistics | |
| Conditional Densities | |
| Expected Values | |
| Properties of Expected Values | |
| The Variance | |
| Properties of Variances | |
| Chebyshev's Inequality | |
| Higher Moments | |
| Moment-Generating Functions | |
| Minitab Applications | |
| Special Distributions | |
| The Poisson Distribution | |
| The Normal Distribution | |
| The Geometric Distribution | |
| The Negative Binomial Distribution | |
| The Gamma Distribution | |
| Minitab Applications | |
| A Proof of the Central Limit Theorem | |
| Estimation | |
| Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments | |
| Interval Estimation | |
| Properties of Estimators | |
| Minimum-Variance Estimators: The Cramer-Rao Lower Bound | |
| Sufficiency | |
| Consistency | |
| Minitab Applications | |
| Hypothesis Testing | |
| The Decision Rule | |
| Testing Binomial Data-H0: p = p | |
| Type I and Type II Errors | |
| A Notion of Optimality: The Generalized Likelihood Ratio | |
| The Normal Distribution | |
| Point Estimates for âÇ m and âÇ s2 | |
| The âÇ c2 Distribution | |
| Inferences about âÇ s2 | |
| The F and t Distributions | |
| Drawing Inferences about âÇ m | |
| Minitab Applications | |
| Some Distribution Results for Y and S | |
| Appendix 7.A.3: A Proof of Theorem 7.3.5 | |
| A Proof That the One-Sample t | |
| Test Is a GLRT | |
| Types of Data: A Brief Overview | |
| Classifying Data | |
| Two-Sample Problems | |
| Testing H 0: = The Two-Sample t Test | |
| Testing H 0: = The F Test | |
| Binomial Data: Testing H 0 px = py | |
| Confidence Intervals for the Two-Sample Problem | |
| A Derivation of the Two-Sample t | |
| Test (A Proof of Theorem 9.2.2.) | |
| Power Calculations for a Two-Sample t Test | |
| Minitab Applications | |
| Goodness-of-Fit Tests | |
| The Multinomial Distribution | |
| Goodness-of-Fit Tests: All Parameters Known | |
| Goodness-of-Fit Tests: Parameters Unknown | |
| Contingency Tables | |
| Minitab Applications | |
| Regression | |
| The Method of Least Squares | |
| The Linear Model | |
| Covariance and Correlation | |
| The Bivariate Normal Distribution | |
| Minitab Applications | |
| A Proof of Theorem 11.3.3 | |
| The Analysis of Variance | |
| The F Test | |
| Multiple Comparisons: Tukey's Method | |
| Testing Subhypotheses with Orthogonal Contrasts | |
| Data Transformations | |
| Minitab Applications | |
| A Proof of Theorem 12.2.2 | |
| The Distribution of $E{ down 12 SSTR/ up 12 (k-1)} over { down 12 SSE/ up 12 (n-k)} | |
| When H1 Is True | |
| Randomized Block Designs | |
| The F Test for a Randomized Block Design | |
| The Paired t Test | |
| Minitab Applications | |
| Nonparametric Statistics | |
| The Sign Test | |
| The Wilcoxon Signed Rank Test | |
| The Kruskal-Wallis Test | |
| The Friedman Test | |
| Minitab Applications | |
| Appendix: Statistical Tables | |
| Answers to Selected Odd-Numbered Questions | |
| Bibliography | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
