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Introduction To Probability
1-4 | Set Theory | Exercises | p.15 |
1-5 | The Definitions of Probability | Exercises | p.21 |
1-6 | Finite Sample Spaces | Exercises | p.25 |
1-7 | Counting Methods | Exercises | p.32 |
1-8 | Combinatorial Methods | Exercises | p.41 |
1-9 | Multinomial Coefficients | Exercises | p.45 |
1-10 | The Probability of a Union of Events | Exercises | p.50 |
Supplementary Exercises | p.53 |
Conditional Probability
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2-1 | The Definition of conditional Probability | Exercises | p.65 |
2-2 | Independent Events | Exercises | p.75 |
2-3 | Bayes' Theorem | Exercises | p.84 |
2-4 | The Gambler's Ruin Problem | Exercises | p.89 |
Supplementary Exercises | p.90 |
Random Variables And Distributions
3-1 | Random Variables and Discrete Distributions | Exercises | p.100 |
3-2 | Continuous Distributions | Exercises | p.106 |
3-3 | The Cumulative Distribution Function | Exercises | p.116 |
3-4 | Bivariate Distributions | Exercises | p.129 |
3-5 | Marginal Distributions | Exercises | p.140 |
3-6 | Conditional Distributions | Exercises | p.151 |
3-7 | Multivariate Distributions | Exercises | p.166 |
3-8 | Functions of a Random Variable | Exercises | p.174 |
3-9 | Functions of Two or More Random Variables | Exercises | p.187 |
3-10 | Markov Chains | Exercises | p.200 |
Supplementary Exercises | p.202 |
Expectation
4-1 | The Expectation of a Random Variable | Exercises | p.216 |
4-2 | Properties of Expectations | Exercises | p.224 |
4-3 | Variance | Exercises | p.233 |
4-4 | Moments | Exercises | p.240 |
4-5 | The Mean and the Median | Exercises | p.247 |
4-6 | Covariance and Correlation | Exercises | p.255 |
4-7 | Conditional Expectation | Exercises | p.264 |
4-8 | Utility | Exercises | p.270 |
Supplementary Exercises | p.272 |
Special Distributions
5-2 | The Bernoulli and Binomial Distributions | Exercises | p.280 |
5-3 | The Hypergeometric Distributions | Exercises | p.287 |
5-4 | The Poisson Distributions | Exercises | p.296 |
5-5 | The Negative Binomial Distributions | Exercises | p.301 |
5-6 | The Normal Distributions | Exercises | p.315 |
5-7 | The Gamma Distributions | Exercises | p.325 |
5-8 | The Beta Distributions | Exercises | p.333 |
5-9 | The Multinomial Distributions | Exercises | p.337 |
5-10 | The Bivariate Normal Distributions | Exercises | p.343 |
Supplementary Exercises | p.345 |
Large Random Samples
6-1 | Introduction | Exercises | p.348 |
6-2 | The Law of Large Numbers | Exercises | p.358 |
6-3 | The Central Limit Theorem | Exercises | p.370 |
6-4 | The Correction for Continuity | Exercises | p.374 |
Supplementary Exercises | p.375 |
Estimation
7-1 | Statistical Inference | Exercises | p.384 |
7-2 | Prior and Posterior Distributions | Exercises | p.393 |
7-3 | Conjugate Prior Distributions | Exercises | p.405 |
7-4 | Bayes Estimators | Exercises | p.416 |
7-5 | Maximum Likelihood Estimators | Exercises | p.425 |
7-6 | Properties of Maximum Likelihood Estimators | Exercises | p.441 |
7-7 | Sufficient Statistics | Exercises | p.448 |
7-8 | Jointly Sufficient Statistics | Exercises | p.454 |
7-9 | Improving an Estimator | Exercises | p.460 |
Supplementary Exercises | p.461 |
Sampling Distributions Of Estimators
8-1 | The Sampling Distribution of a Statistic | Exercises | p.468 |
8-2 | The Chi-Square Distributions | Exercises | p.472 |
8-3 | Joint Distribution of the Sample Mean and Sample Variance | Exercises | p.479 |
8-4 | The t Distribution | Exercises | p.484 |
8-5 | Confidence Intervals | Exercises | p.494 |
8-6 | Bayesian Analysis of Samples from a Normal Distribution | Exercises | p.505 |
8-7 | Unbiased Estimators | Exercises | p.512 |
8-8 | Fisher Information | Exercises | p.527 |
Supplementary Exercises | p.528 |
Testing Hypotheses
9-1 | Problem of Testing Hypotheses | Exercises | p.548 |
9-2 | Testing Simple Hypotheses | Exercises | p.557 |
9-3 | Uniformly Most Powerful Tests | Exercises | p.566 |
9-4 | Two-Sided Alternatives | Exercises | p.575 |
9-5 | The t Test | Exercises | p.585 |
9-6 | Comparing the Means of Two Normal Distributions | Exercises | p.596 |
9-7 | The F Distributions | Exercises | p.604 |
9-8 | Bayes Test Procedures | Exercises | p.615 |
9-9 | Foundational Issues | Exercises | p.620 |
Supplementary Exercises | p.621 |
Categorical Data And Nonparametric Methods
10-1 | Tests of Goodness-of-Fit | Exercises | p.632 |
10-2 | Goodness-of-Fit for Composite Hypotheses | Exercises | p.640 |
10-3 | Contingency Tables | Exercises | p.645 |
10-4 | Tests of Homogeneity | Exercises | p.652 |
10-5 | Simpson's Paradox | Exercises | p.656 |
10-6 | Kolmogorov-Smirnov Tests | Exercises | p.665 |
10-7 | Robust Estimation | Exercises | p.677 |
10-8 | Sign and Rank Tests | Exercises | p.684 |
Supplementary Exercises | p.686 |
Linear Statistical Models
11-1 | The Method of Least Squares | Exercises | p.697 |
11-2 | Regression | Exercises | p.706 |
11-3 | Statistical Inference in Simple Linear Regression | Exercises | p.727 |
11-4 | Bayesian Inference in Simple Linear Regression | Exercises | p.735 |
11-5 | The General Linear Model and Multiple Regression | Exercises | p.752 |
11-6 | Analysis of Variance | Exercises | p.761 |
11-7 | The Two-Way Layout | Exercises | p.771 |
11-8 | The Two-Way Layout with Replications | Exercises | p.781 |
Supplementary Exercises | p.783 |
Simulation
12-1 | What is Simulation? | Exercises | p.791 |
12-2 | Why is Simulation Useful? | Exercises | p.802 |
12-3 | Simulating Specific Distributions | Exercises | p.815 |
12-4 | Importance Sampling | Exercises | p.821 |
12-5 | Markov Chain Monte Carlo | Exercises | p.836 |
12-6 | The Bootstrap | Exercises | p.849 |
Supplementary Exercises | p.850 |