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### We start by introducing mathematical concept of a probability space. 1.1 Sample Space and Events. Probability theory is mainly concerned with random experiments. Definition 1.1 (Random modern probability theory. Definition 1.5

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In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform. This is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.