- (v) When one does multiple integrals
by Monte Carlo and chooses a set of
**n**points where for**i**, one chooses separately randomly. This gives distributed randomly over the plane. - It would be wrong to view as in Newton
Cotes as an integral over
**x**of where we think of doing**x**and**y**integrals by Monte Carlo. - This incorrect approach gives a set of points where
one first chooses randomly, then fixing this value of ,
chooses random values of
**y**; then change to a new random**x**and so on. - This scenario gives use to a set where
- In this case error is proportional to and NOT where all and all are chosen independently.

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