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The correlation coefficients (Pearson's) is usually defined in terms of discrete sampling of a function. However, I have seen that the mean and standard deviation, for example, are also typically written in terms of discrete variables BUT may also be expressed in terms of a continuous probability distribution. e.g. the mean may be written as \mu_x = \int x p(x) dx.

So my question is, does there exist a similar formalism for the correlation coefficient between two continuous probability distributions? Any help would be greatly appreciated on this issue for which many Google searches came up empty handed. :-)

Natski