A Probability and Statistics Companion

ISBN: 9780470471951 出版年：2009 页码：278 John J Kinney Wiley

Preface. 1. Probability and Sample Spaces. Why Study Probability? Probability. Sample Spaces. Some Properties of Probabilities. Finding Probabilities of Events. Conclusions. Explorations. 2. Permutations and Combinations: Choosing the Best Candidate Acceptance Sampling. Permutations. Counting Principle. Permutations with Some Objects Alike. Permuting Only Some of the Objects. Combinations. General Addition Theorem and Applications. Conclusions. Explorations. 3. Conditional Probability. Introduction. Some Notation. Bayes' Theorem. Conclusions. Explorations. 4. Geometric Probability. Conclusion. Explorations. 5. Random Variables and Discrete Probability Distributions-Uniform, Binomial, Hypergeometric, and Geometric Distributions. Introduction. Discrete Uniform Distribution. Mean and Variance of a Discrete Random Variable. Intervals, sigma , and German Tanks. Sums. Binomial Probability Distribution. Mean and Variance of the Binomial Distribution. Sums. Hypergeometric Distribution. Other Properties of the Hypergeometric Distribution. Geometric Probability Distribution. Conclusions. Explorations. 6. Seven-Game Series in Sports. Introduction. Seven-Game Series. Winning the First Game. How Long Should the Series Last? Conclusions. Explorations. 7. Waiting Time Problems. Waiting for the First Success. The Mythical Island. Waiting for the Second Success. Waiting for the r th Success. Mean of the Negative Binomial. Collecting Cereal Box Prizes. Heads Before Tails. Waiting for Patterns. Expected Waiting Time for HH. Expected Waiting Time for TH. An Unfair Game with a Fair Coin. Three Tosses. Who Pays for Lunch? Expected Number of Lunches. Negative Hypergeometric Distribution. Mean and Variance of the Negative Hypergeometric. Negative Binomial Approximation. The Meaning of the Mean. First Occurrences. Waiting Time for c Special Items to Occur. Estimating k. Conclusions. Explorations. 8. Continuous Probability Distributions: Sums, the Normal Distribution, and the Central Limit Theorem Bivariate Random Variables. Uniform Random Variable. Sums. A Fact About Means. Normal Probability Distribution. Facts About Normal Curves. Bivariate Random Variables. Variance. Central Limit Theorem: Sums. Central Limit Theorem: Means. Central Limit Theorem. Expected Values and Bivariate Random Variables. Means and Variances of Means. A Note on the Uniform Distribution. Conclusions. Explorations. 9. Statistical Inference I. Estimation. Confidence Intervals. Hypothesis Testing. beta and the Power of a Test. p -Value for a Test. Conclusions. Explorations. 10. Statistical Inference II: Continuous Probability Distributions II-Comparing Two Samples. The Chi-Squared Distribution. Statistical Inference on the Variance. Student t Distribution. Testing the Ratio of Variances: The F Distribution. Tests on Means from Two Samples. Conclusions. Explorations. 11. Statistical Process Control. Control Charts. Estimating sigma Using the Sample Standard Deviations. Estimating sigma Using the Sample Ranges. Control Charts for Attributes. np Control Chart. p Chart. Some Characteristics of Control Charts. Some Additional Tests for Control Charts. Conclusions. Explorations. 12. Nonparametric Methods. Introduction. The Rank Sum Test. Order Statistics. Median. Maximum. Runs. Some Theory of Runs. Conclusions. Explorations. 13. Least Squares, Medians, and the Indy 500. Introduction. Least Squares. Principle of Least Squares. Influential Observations. The Indy 500. A Test for Linearity: The Analysis of Variance. A Caution. Nonlinear Models. The Median-Median Line. When Are the Lines Identical? Determining the Median-Median Line. Analysis for Years 1911-1969. Conclusions. Explorations. 14. Sampling. Simple Random Sampling. Stratification. Proportional Allocation. Optimal Allocation. Some Practical Considerations. Strata. Conclusions. Explorations. 15. Design of Experiments. Yates Algorithm. Randomization and Some Notation. Confounding. Multiple Observations. Design Models and Multiple Regression Models. Testing the Effects for Significance. Conclusions. Explorations. 16. Recursions and Probability. Introduction. Conclusions. Explorations. 17. Generating Functions and the Central Limit Theorem. Means and Variances. A Normal Approximation. Conclusions. Explorations. Bibliography. Where to Learn More. Index.