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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 | |