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This accessible and easy-to-read book provides many examples to illustrate diverse topics in probability and statistics, from initial concepts up to advanced calculations. Special attention is devoted e.g. to independency of events, inequalities in probability and functions of random variables. The book is directed to students of mathematics, statistics, engineering, and other quantitative sciences, in particular to readers who need or want to learn by self-study. The author is convinced that sophisticated examples are more useful for the student than a lengthy formalism treating the greatest possible generality. Contents:Mathematics revisionIntroduction to probabilityFinite sample spacesConditional probability and independenceOne-dimensional random variablesFunctions of random variablesBi-dimensional random variablesCharacteristics of random variablesDiscrete probability modelsContinuous probability modelsGenerating functions in probabilitySums of many random variablesSamples and sampling distributionsEstimation of parametersHypothesis tests

Probabilities. --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistical methods --- Convergence of random variables. --- Generating functions. --- Order statistics. --- Probability measures. --- Statistical applications. --- Transforms of random variables. --- Univariate and multivariate models.