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- Then, the new Central Limit Theorem states that the pair (F,G)
is asymptotically a (two-dimensional) Gaussian distribution with
probability distribution
- where we have lapsed into a vector notation:
and matrix 
.
- Proof: Just as in ordinary central limit theorem, except
you consider two-dimensional characteristic function
.
- This extension is important as it allows you to use correlations
between functions calculated from the same data (observations).
Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu