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Numerical experiments and the covariance

We will call these values our measurements and the entire set as our measured sample. The action of measuring all the elements of a sample we will call a stochastic experiment (since, operationally, they are often associated with results of empirical observation of some physical or mathematical phenomena; precisely an experiment). We assume that these values are distributed according to some PDF p_X^{\phantom X}(x) , where X is just the formal symbol for the stochastic variable whose PDF is p_X^{\phantom X}(x) . Instead of trying to determine the full distribution p we are often only interested in finding the few lowest moments, like the mean \mu_X^{\phantom X} and the variance \sigma_X^{\phantom X} .