- This extended theorem reads:
- If are independent random variables with
possibly different distributions, and:
- where
*must*exist (not necessary in Laplace's version where all had same distribution). - Let
- Then
*if*, - then
**y**is Gaussianly distributed with- mean and
- standard deviation .

- Note the does when exists in Laplace's case as and .

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu