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 \( \sigma_X^{\phantom X} \).