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Why probability and statistics? | |
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Biometry: iris recognition | |
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Killer football | |
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Cars and goats: the Monty Hall dilemma | |
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The space shuttle Challenger | |
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Statistics versus intelligence agencies | |
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The speed of light | |
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Outcomes, events, and probability | |
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Sample spaces | |
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Events | |
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Probability | |
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Products of sample spaces | |
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An infinite sample space | |
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Solutions to the quick exercises | |
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Exercises | |
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Conditional probability and independence | |
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Conditional probability | |
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The multiplication rule | |
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The law of total probability and Bayes' rule | |
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Independence | |
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Solutions to the quick exercises | |
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Exercises | |
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Discrete random variables | |
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Random variables | |
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The probability distribution of a discrete random variable | |
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The Bernoulli and binomial distributions | |
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The geometric distribution | |
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Solutions to the quick exercises | |
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Exercises | |
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Continuous random variables | |
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Probability density functions | |
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The uniform distribution | |
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The exponential distribution | |
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The Pareto distribution | |
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The normal distribution | |
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Quantiles | |
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Solutions to the quick exercises | |
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Exercises | |
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Simulation | |
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What is simulation? | |
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Generating realizations of random variables | |
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Comparing two jury rules | |
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The single-server queue | |
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Solutions to the quick exercises | |
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Exercises | |
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Expectation and variance | |
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Expected values | |
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Three examples | |
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The change-of-variable formula | |
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Variance | |
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Solutions to the quick exercises | |
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Exercises | |
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Computations with random variables | |
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Transforming discrete random variables | |
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Transforming continuous random variables | |
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Jensen's inequality | |
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Extremes | |
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Solutions to the quick exercises | |
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Exercises | |
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Joint distributions and independence | |
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Joint distributions of discrete random variables | |
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Joint distributions of continuous random variables | |
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More than two random variables | |
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Independent random variables | |
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Propagation of independence | |
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Solutions to the quick exercises | |
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Exercises | |
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Covariance and correlation | |
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Expectation and joint distributions | |
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Covariance | |
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The correlation coefficient | |
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Solutions to the quick exercises | |
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Exercises | |
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More computations with more random variables | |
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Sums of discrete random variables | |
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Sums of continuous random variables | |
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Product and quotient of two random variables | |
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Solutions to the quick exercises | |
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Exercises | |
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The Poisson process | |
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Random points | |
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Taking a closer look at random arrivals | |
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The one-dimensional Poisson process | |
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Higher-dimensional Poisson processes | |
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Solutions to the quick exercises | |
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Exercises | |
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The law of large numbers | |
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Averages vary less | |
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Chebyshev's inequality | |
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The law of large numbers | |
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Consequences of the law of large numbers | |
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Solutions to the quick exercises | |
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Exercises | |
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The central limit theorem | |
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Standardizing averages | |
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Applications of the central limit theorem | |
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Solutions to the quick exercises | |
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Exercises | |
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Exploratory data analysis: graphical summaries | |
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Example: the Old Faithful data | |
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Histograms | |
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Kernel density estimates | |
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The empirical distribution function | |
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Scatterplot | |
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Solutions to the quick exercises | |
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Exercises | |
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Exploratory data analysis: numerical summaries | |
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The center of a dataset | |
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The amount of variability of a dataset | |
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Empirical quantiles, quartiles, and the IQR | |
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The box-and-whisker plot | |
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Solutions to the quick exercises | |
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Exercises | |
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Basic statistical models | |
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Random samples and statistical models | |
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Distribution features and sample statistics | |
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Estimating features of the "true" distribution | |
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The linear regression model | |
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Solutions to the quick exercises | |
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Exercises | |
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The bootstrap | |
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The bootstrap principle | |
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The empirical bootstrap | |
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The parametric bootstrap | |
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Solutions to the quick exercises | |
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Exercises | |
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Unbiased estimators | |
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Estimators | |
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Investigating the behavior of an estimator | |
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The sampling distribution and unbiasedness | |
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Unbiased estimators for expectation and variance | |
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Solutions to the quick exercises | |
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Exercises | |
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Efficiency and mean squared error | |
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Estimating the number of German tanks | |
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Variance of an estimator | |
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Mean squared error | |
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Solutions to the quick exercises | |
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Exercises | |
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Maximum likelihood | |
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Why a general principle? | |
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The maximum likelihood principle | |
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Likelihood and loglikelihood | |
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Properties of maximum likelihood estimators | |
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Solutions to the quick exercises | |
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Exercises | |
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The method of least squares | |
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Least squares estimation and regression | |
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Residuals | |
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Relation with maximum likelihood | |
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Solutions to the quick exercises | |
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Exercises | |
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Confidence intervals for the mean | |
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General principle | |
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Normal data | |
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Bootstrap confidence intervals | |
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Large samples | |
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Solutions to the quick exercises | |
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Exercises | |
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More on confidence intervals | |
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The probability of success | |
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Is there a general method? | |
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One-sided confidence intervals | |
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Determining the sample size | |
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Solutions to the quick exercises | |
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Exercises | |
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Testing hypotheses: essentials | |
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Null hypothesis and test statistic | |
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Tail probabilities | |
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Type I and type II errors | |
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Solutions to the quick exercises | |
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Exercises | |
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Testing hypotheses: elaboration | |
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Significance level | |
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Critical region and critical values | |
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Type II error | |
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Relation with confidence intervals | |
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Solutions to the quick exercises | |
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Exercises | |
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The t-test | |
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Monitoring the production of ball bearings | |
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The one-sample t-test | |
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The t-test in a regression setting | |
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Solutions to the quick exercises | |
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Exercises | |
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Comparing two samples | |
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Is dry drilling faster than wet drilling? | |
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Two samples with equal variances | |
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Two samples with unequal variances | |
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Large samples | |
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Solutions to the quick exercises | |
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Exercises | |
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Summary of distributions | |
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Tables of the normal and t-distributions | |
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Answers to selected exercises | |
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Full solutions to selected exercises | |
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References | |
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List of symbols | |
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Index | |