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Given n-dimensional distribution
:
- The mean now becomes an n-dimensional vector

- The variance becomes an
moment matrix
M

- Note for we can show---analogously to Equation (9)---that

- Also note that M is symmetric and positive semi-definite.
[This follows because
---any y---clearly has a
integrand].
- Now the diagonal terms of M are called variances which are
:
- Their square roots are standard deviations again.
- Further, when
, we put
,
which is
and is called the correlation coefficient.
Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu