Means---Moments---Correlations for Multidimensional Distributions II

• Note that if ---all ---then we say that are uncorrelated.

• Further, if are independent, then Equation (10) shows at once that they are uncorrelated.

• The converse does not follow of course (except under special circumstances, e.g., if Gaussianly distributed).

• One can define higher order tensors but these are not too important as in usual applications are n functions of N>>n observations.

  Then central limit theorem---to which we will come---implies that only the mean and are important asymptotically (in N).