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Preface | p. V |
Introduction | p. 1 |
Equally Likely Outcomes | p. 2 |
Interpretations | p. 11 |
Distributions | p. 19 |
Conditional Probability and Independence | p. 33 |
Bayes' Rule | p. 47 |
Sequences of Events | p. 56 |
Summary | p. 73 |
Review Exercises | p. 74 |
Repeated Trials and Sampling | p. 79 |
The Binomial Distribution | p. 80 |
Normal Approximation: Method | p. 93 |
Normal Approximation: Derivation (Optional) | p. 111 |
Poisson Approximation | p. 117 |
Random Sampling | p. 123 |
Summary | p. 130 |
Review Exercises | p. 132 |
Random Variables | p. 139 |
Introduction | p. 139 |
Expectation | p. 162 |
Standard Deviation and Normal Approximation | p. 185 |
Discrete Distributions | p. 208 |
The Poisson Distribution | p. 222 |
Symmetry (Optional) | p. 237 |
Summary | p. 248 |
Review Exercises | p. 250 |
Continuous Distributions | p. 259 |
Probability Densities | p. 260 |
Exponential and Gamma Distributions | p. 278 |
Hazard Rates (Optional) | p. 296 |
Change of Variable | p. 302 |
Cumulative Distribution Functions | p. 311 |
Order Statistics (Optional) | p. 325 |
Summary | p. 334 |
Review Exercises | p. 336 |
Continuous Joint Distributions | p. 339 |
Uniform Distributions | p. 340 |
Densities | p. 346 |
Independent Normal Variables | p. 357 |
Operations (Optional) | p. 371 |
Summary | p. 386 |
Review Exercises | p. 387 |
Dependence | p. 393 |
Conditional Distributions: Discrete Case | p. 393 |
Conditional Expectation: Discrete Case | p. 401 |
Conditioning: Density Case | p. 410 |
Covariance and Correlation | p. 430 |
Bivariate Normal | p. 449 |
Summary | p. 464 |
Review Exercises | p. 466 |
Distribution Summaries | p. 475 |
Discrete | p. 476 |
Continuous | p. 477 |
Beta | p. 478 |
Binomial | p. 479 |
Exponential | p. 480 |
Gamma | p. 481 |
Geometric and Negative Binomial | p. 482 |
Hypergeometric | p. 483 |
Normal | p. 484 |
Poisson | p. 486 |
Uniform | p. 487 |
Examinations | p. 489 |
Solutions to Examinations | p. 498 |
Appendices | p. 505 |
Counting | p. 507 |
Sums | p. 515 |
Calculus | p. 517 |
Exponents and Logarithms | p. 525 |
Normal Table | p. 531 |
Brief Solutions to Odd-Numbered Exercises | p. 533 |
Index | p. 549 |
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