Probability and statistics /
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| Author / Creator: | DeGroot, Morris H., 1931-1989 |
|---|---|
| Edition: | 3rd ed. |
| Imprint: | Boston : Addison-Wesley, c2002. |
| Description: | xv, 816 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5360730 |
Table of Contents:
- 1. Introduction to Probability
- The History of Probability
- Interpretations of Probability
- Experiments and Events
- Set Theory
- The Definition of Probability
- Finite Sample Spaces
- Counting Methods
- Combinatorial Methods
- Multinomial Coefficients
- The Probability of a Union of Events
- Statistical Swindles
- Supplementary Exercises
- 2. Conditional Probability
- The Definition of Conditional Probability
- Independent Events
- Bayes' Theorem
- Markov Chains
- The Gambler's Ruin Problem
- Supplementary Exercises
- 3. Random Variables and Distribution
- Random Variables and Discrete Distributions
- Continuous Distributions
- The Distribution Function
- Bivariate Distributions
- Marginal Distributions
- Conditional Distributions
- Multivariate Distributions
- Functions of a Random Variable
- Functions of Two or More Random Variables
- Supplementary Exercises
- 4. Expectation
- The Expectation of a Random Variable
- Properties of Expectations
- Variance
- Moments
- The Mean and The Median
- Covariance and Correlation
- Conditional Expectation
- The Sample Mean
- Utility
- Supplementary Exercises
- 5. Special Distributions
- Introduction
- The Bernoulli and Binomial Distributions
- The Hypergeometric Distribution
- The Poisson Distribution
- The Negative Binomial Distribution
- The Normal Distribution
- The Central Limit Theorem
- The Correction for Continuity
- The Gamma Distribution
- The Beta Distribution
- The Multinomial Distribution
- The Bivariate Normal Distribution
- Supplementary Exercises
- 6. Estimation
- Statistical Inference
- Prior and Posterior Distributions
- Conjugate Prior Distributions
- Bayes Estimators
- Maximum Likelihood Estimators
- Properties of Maximum Likelihood Estimators
- Sufficient Statistics
- Jointly Sufficient Statistics
- Improving an Estimator
- Supplementary Exercises
- 7. Sampling Distributions of Estimators
- The Sampling Distribution of a Statistic
- The Chi-Square Distribution
- Joint Distribution of the Sample Mean and Sample Variance
- The t Distribution
- Confidence Intervals
- Bayesian Analysis of Samples from a Normal Distribution
- Unbiased Estimators
- Fisher Information
- Supplementary Exercises
- 8. Testing Hypotheses
- Problems of Testing Hypotheses
- Testing Simple Hypotheses
- Uniformly Most Powerful Tests
- Two-Sided Alternatives
- The t Test
- Comparing the Means of Two Normal Distributions
- The F Distribution
- Bayes Test Procedures
- Foundational Issues
- Supplementary Exercises
- 9. Categorical Data and Nonparametric Methods
- Tests of Goodness-of-Fit
- Goodness-of-Fit for Composite Hypotheses
- Contingency Tables
- Tests of Homogeneit
- Simpson's Paradox
- Kolmogorov-Smirnov Test
- Robust Estimation
- Sign and Rank Tests
- Supplementary Exercises
- 10. Linear Statistical Models
- The Method of Least Squares
- Regression
- Statistical Inference in Simple Linear Regression
- Bayesian Inference in Simple Linear Regression
- The General Linear Model and Multiple Regression
- Analysis of Variance
- The Two-Way Layout
- The Two-Way Layout with Replications
- Supplementary Exercises
- 11. Simulation
- Why is Simulation Useful?
- Simulating Specific Distributions
- Importance Sampling
- Markov Chain Monte Carlo
- The Bootstrap
- Supplementary Exercises
