Why probability and statistics? | p. 1 |
Biometry: iris recognition | p. 1 |
Killer football | p. 3 |
Cars and goats: the Monty Hall dilemma | p. 4 |
The space shuttle Challenger | p. 5 |
Statistics versus intelligence agencies | p. 7 |
The speed of light | p. 9 |
Outcomes, events, and probability | p. 13 |
Sample spaces | p. 13 |
Events | p. 14 |
Probability | p. 16 |
Products of sample spaces | p. 18 |
An infinite sample space | p. 19 |
Solutions to the quick exercises | p. 21 |
Exercises | p. 21 |
Conditional probability and independence | p. 25 |
Conditional probability | p. 25 |
The multiplication rule | p. 27 |
The law of total probability and Bayes' rule | p. 30 |
Independence | p. 32 |
Solutions to the quick exercises | p. 35 |
Exercises | p. 37 |
Discrete random variables | p. 41 |
Random variables | p. 41 |
The probability distribution of a discrete random variable | p. 43 |
The Bernoulli and binomial distributions | p. 45 |
The geometric distribution | p. 48 |
Solutions to the quick exercises | p. 50 |
Exercises | p. 51 |
Continuous random variables | p. 57 |
Probability density functions | p. 57 |
The uniform distribution | p. 60 |
The exponential distribution | p. 61 |
The Pareto distribution | p. 63 |
The normal distribution | p. 64 |
Quantiles | p. 65 |
Solutions to the quick exercises | p. 67 |
Exercises | p. 68 |
Simulation | p. 71 |
What is simulation? | p. 71 |
Generating realizations of random variables | p. 72 |
Comparing two jury rules | p. 75 |
The single-server queue | p. 80 |
Solutions to the quick exercises | p. 84 |
Exercises | p. 85 |
Expectation and variance | p. 89 |
Expected values | p. 89 |
Three examples | p. 93 |
The change-of-variable formula | p. 94 |
Variance | p. 96 |
Solutions to the quick exercises | p. 99 |
Exercises | p. 99 |
Computations with random variables | p. 103 |
Transforming discrete random variables | p. 103 |
Transforming continuous random variables | p. 104 |
Jensen's inequality | p. 106 |
Extremes | p. 108 |
Solutions to the quick exercises | p. 110 |
Exercises | p. 111 |
Joint distributions and independence | p. 115 |
Joint distributions of discrete random variables | p. 115 |
Joint distributions of continuous random variables | p. 118 |
More than two random variables | p. 122 |
Independent random variables | p. 124 |
Propagation of independence | p. 125 |
Solutions to the quick exercises | p. 126 |
Exercises | p. 127 |
Covariance and correlation | p. 135 |
Expectation and joint distributions | p. 135 |
Covariance | p. 138 |
The correlation coefficient | p. 141 |
Solutions to the quick exercises | p. 143 |
Exercises | p. 144 |
More computations with more random variables | p. 151 |
Sums of discrete random variables | p. 151 |
Sums of continuous random variables | p. 154 |
Product and quotient of two random variables | p. 159 |
Solutions to the quick exercises | p. 162 |
Exercises | p. 163 |
The Poisson process | p. 167 |
Random points | p. 167 |
Taking a closer look at random arrivals | p. 168 |
The one-dimensional Poisson process | p. 171 |
Higher-dimensional Poisson processes | p. 173 |
Solutions to the quick exercises | p. 176 |
Exercises | p. 176 |
The law of large numbers | p. 181 |
Averages vary less | p. 181 |
Chebyshev's inequality | p. 183 |
The law of large numbers | p. 185 |
Consequences of the law of large numbers | p. 188 |
Solutions to the quick exercises | p. 191 |
Exercises | p. 191 |
The central limit theorem | p. 195 |
Standardizing averages | p. 195 |
Applications of the central limit theorem | p. 199 |
Solutions to the quick exercises | p. 202 |
Exercises | p. 203 |
Exploratory data analysis: graphical summaries | p. 207 |
Example: the Old Faithful data | p. 207 |
Histograms | p. 209 |
Kernel density estimates | p. 212 |
The empirical distribution function | p. 219 |
Scatterplot | p. 221 |
Solutions to the quick exercises | p. 225 |
Exercises | p. 226 |
Exploratory data analysis: numerical summaries | p. 231 |
The center of a dataset | p. 231 |
The amount of variability of a dataset | p. 233 |
Empirical quantiles, quartiles, and the IQR | p. 234 |
The box-and-whisker plot | p. 236 |
Solutions to the quick exercises | p. 238 |
Exercises | p. 240 |
Basic statistical models | p. 245 |
Random samples and statistical models | p. 245 |
Distribution features and sample statistics | p. 248 |
Estimating features of the "true" distribution | p. 253 |
The linear regression model | p. 256 |
Solutions to the quick exercises | p. 259 |
Exercises | p. 259 |
The bootstrap | p. 269 |
The bootstrap principle | p. 269 |
The empirical bootstrap | p. 272 |
The parametric bootstrap | p. 276 |
Solutions to the quick exercises | p. 279 |
Exercises | p. 280 |
Unbiased estimators | p. 285 |
Estimators | p. 285 |
Investigating the behavior of an estimator | p. 287 |
The sampling distribution and unbiasedness | p. 288 |
Unbiased estimators for expectation and variance | p. 292 |
Solutions to the quick exercises | p. 294 |
Exercises | p. 294 |
Efficiency and mean squared error | p. 299 |
Estimating the number of German tanks | p. 299 |
Variance of an estimator | p. 302 |
Mean squared error | p. 305 |
Solutions to the quick exercises | p. 307 |
Exercises | p. 307 |
Maximum likelihood | p. 313 |
Why a general principle? | p. 313 |
The maximum likelihood principle | p. 314 |
Likelihood and loglikelihood | p. 316 |
Properties of maximum likelihood estimators | p. 321 |
Solutions to the quick exercises | p. 322 |
Exercises | p. 323 |
The method of least squares | p. 329 |
Least squares estimation and regression | p. 329 |
Residuals | p. 332 |
Relation with maximum likelihood | p. 335 |
Solutions to the quick exercises | p. 336 |
Exercises | p. 337 |
Confidence intervals for the mean | p. 341 |
General principle | p. 341 |
Normal data | p. 345 |
Bootstrap confidence intervals | p. 350 |
Large samples | p. 353 |
Solutions to the quick exercises | p. 355 |
Exercises | p. 356 |
More on confidence intervals | p. 361 |
The probability of success | p. 361 |
Is there a general method? | p. 364 |
One-sided confidence intervals | p. 366 |
Determining the sample size | p. 367 |
Solutions to the quick exercises | p. 368 |
Exercises | p. 369 |
Testing hypotheses: essentials | p. 373 |
Null hypothesis and test statistic | p. 373 |
Tail probabilities | p. 376 |
Type I and type II errors | p. 377 |
Solutions to the quick exercises | p. 379 |
Exercises | p. 380 |
Testing hypotheses: elaboration | p. 383 |
Significance level | p. 383 |
Critical region and critical values | p. 386 |
Type II error | p. 390 |
Relation with confidence intervals | p. 392 |
Solutions to the quick exercises | p. 393 |
Exercises | p. 394 |
The t-test | p. 399 |
Monitoring the production of ball bearings | p. 399 |
The one-sample t-test | p. 401 |
The t-test in a regression setting | p. 405 |
Solutions to the quick exercises | p. 409 |
Exercises | p. 410 |
Comparing two samples | p. 415 |
Is dry drilling faster than wet drilling? | p. 415 |
Two samples with equal variances | p. 416 |
Two samples with unequal variances | p. 419 |
Large samples | p. 422 |
Solutions to the quick exercises | p. 424 |
Exercises | p. 424 |
Summary of distributions | p. 429 |
Tables of the normal and t-distributions | p. 431 |
Answers to selected exercises | p. 435 |
Full solutions to selected exercises | p. 445 |
References | p. 475 |
List of symbols | p. 477 |
Index | p. 479 |
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